Intrinsic neural diversity quenches the dynamic volatility of neural networks.

Heterogeneity is the norm in biology. The brain is no different: Neuronal cell types are myriad, reflected through their cellular morphology, type, excitability, connectivity motifs, and ion channel distributions. While this biophysical diversity enriches neural systems' dynamical repertoire, it remains challenging to reconcile with the robustness and persistence of brain function over time (resilience). To better understand the relationship between excitability heterogeneity (variability in excitability within a population of neurons) and resilience, we analyzed both analytically and numerically a nonlinear sparse neural network with balanced excitatory and inhibitory connections evolving over long time scales. Homogeneous networks demonstrated increases in excitability, and strong firing rate correlations-signs of instability-in response to a slowly varying modulatory fluctuation. Excitability heterogeneity tuned network stability in a context-dependent way by restraining responses to modulatory challenges and limiting firing rate correlations, while enriching dynamics during states of low modulatory drive. Excitability heterogeneity was found to implement a homeostatic control mechanism enhancing network resilience to changes in population size, connection probability, strength and variability of synaptic weights, by quenching the volatility (i.e., its susceptibility to critical transitions) of its dynamics. Together, these results highlight the fundamental role played by cell-to-cell heterogeneity in the robustness of brain function in the face of change.

Selective control of synaptic plasticity in heterogeneous networks through transcranial alternating current stimulation (tACS).

Transcranial alternating current stimulation (tACS) represents a promising non-invasive treatment for an increasingly wide range of neurological and neuropsychiatric disorders. The ability to use periodically oscillating electric fields to non-invasively engage neural dynamics opens up the possibility of recruiting synaptic plasticity and to modulate brain function. However, despite consistent reports about tACS clinical effectiveness, strong state-dependence combined with the ubiquitous heterogeneity of cortical networks collectively results in high outcome variability. Introducing variations in intrinsic neuronal timescales, we explored how such heterogeneity influences stimulation-induced change in synaptic connectivity. We examined how spike timing dependent plasticity, at the level of cells, intra- and inter-laminar cortical networks, can be selectively and preferentially engaged by periodic stimulation. Using leaky integrate-and-fire neuron models, we analyzed cortical circuits comprised of multiple cell-types, alongside superficial multi-layered networks expressing distinct layer-specific timescales. Our results show that mismatch in neuronal timescales within and/or between cells-and the resulting variability in excitability, temporal integration properties and frequency tuning-enables selective and directional control on synaptic connectivity by tACS. Our work provides new vistas on how to recruit neural heterogeneity to guide brain plasticity using non-invasive stimulation paradigms.

Diversity-induced trivialization and resilience of neural dynamics.

Heterogeneity is omnipresent across all living systems. Diversity enriches the dynamical repertoire of these systems but remains challenging to reconcile with their manifest robustness and dynamical persistence over time, a fundamental feature called resilience. To better understand the mechanism underlying resilience in neural circuits, we considered a nonlinear network model, extracting the relationship between excitability heterogeneity and resilience. To measure resilience, we quantified the number of stationary states of this network, and how they are affected by various control parameters. We analyzed both analytically and numerically gradient and non-gradient systems modeled as non-linear sparse neural networks evolving over long time scales. Our analysis shows that neuronal heterogeneity quenches the number of stationary states while decreasing the susceptibility to bifurcations: a phenomenon known as trivialization. Heterogeneity was found to implement a homeostatic control mechanism enhancing network resilience to changes in network size and connection probability by quenching the system's dynamic volatility.

Activity-dependent myelination: A glial mechanism of oscillatory self-organization in large-scale brain networks.

Communication and oscillatory synchrony between distributed neural populations are believed to play a key role in multiple cognitive and neural functions. These interactions are mediated by long-range myelinated axonal fiber bundles, collectively termed as white matter. While traditionally considered to be static after development, white matter properties have been shown to change in an activity-dependent way through learning and behavior-a phenomenon known as white matter plasticity. In the central nervous system, this plasticity stems from oligodendroglia, which form myelin sheaths to regulate the conduction of nerve impulses across the brain, hence critically impacting neural communication. We here shift the focus from neural to glial contribution to brain synchronization and examine the impact of adaptive, activity-dependent changes in conduction velocity on the large-scale phase synchronization of neural oscillators. Using a network model based on primate large-scale white matter neuroanatomy, our computational and mathematical results show that such plasticity endows white matter with self-organizing properties, where conduction delay statistics are autonomously adjusted to ensure efficient neural communication. Our analysis shows that this mechanism stabilizes oscillatory neural activity across a wide range of connectivity gain and frequency bands, making phase-locked states more resilient to damage as reflected by diffuse decreases in connectivity. Critically, our work suggests that adaptive myelination may be a mechanism that enables brain networks with a means of temporal self-organization, resilience, and homeostasis.

Arousal Fluctuations Govern Oscillatory Transitions Between Dominant [Formula: see text] and [Formula: see text] Occipital Activity During Eyes Open/Closed Conditions.

Arousal results in widespread activation of brain areas to increase their response in task and behavior relevant ways. Mediated by the Ascending Reticular Arousal System (ARAS), arousal-dependent inputs interact with neural circuitry to shape their dynamics. In the occipital cortex, such inputs may trigger shifts between dominant oscillations, where [Formula: see text] activity is replaced by [Formula: see text] activity, or vice versa. A salient example of this are spectral power alternations observed while eyes are opened and/or closed. These transitions closely follow fluctuations in arousal, suggesting a common origin. To better understand the mechanisms at play, we developed and analyzed a computational model composed of two modules: a thalamocortical feedback circuit coupled with a superficial cortical network. Upon activation by noise-like inputs originating from the ARAS, our model is able to demonstrate that noise-driven non-linear interactions mediate transitions in dominant peak frequency, resulting in the simultaneous suppression of [Formula: see text] limit cycle activity and the emergence of [Formula: see text] oscillations through coherence resonance. Reduction in input provoked the reverse effect - leading to anticorrelated transitions between [Formula: see text] and [Formula: see text] power. Taken together, these results shed a new light on how arousal shapes oscillatory brain activity.

White matter plasticity and maturation in human cognition.

White matter plasticity likely plays a critical role in supporting cognitive development. However, few studies have used the imaging methods specific to white matter tissue structure or experimental designs sensitive to change in white matter necessary to elucidate these relations. Here we briefly review novel imaging approaches that provide more specific information regarding white matter microstructure. Furthermore, we highlight recent studies that provide greater clarity regarding the relations between changes in white matter and cognition maturation in both healthy children and adolescents and those with white matter insult. Finally, we examine the hypothesis that white matter is linked to cognitive function via its impact on neural synchronization. We test this hypothesis in a population of children and adolescents with recurrent demyelinating syndromes. Specifically, we evaluate group differences in white matter microstructure within the optic radiation; and neural phase synchrony in visual cortex during a visual task between 25 patients and 28 typically developing age-matched controls. Children and adolescents with demyelinating syndromes show evidence of myelin and axonal compromise and this compromise predicts reduced phase synchrony during a visual task compared to typically developing controls. We investigate one plausible mechanism at play in this relationship using a computational model of gamma generation in early visual cortical areas. Overall, our findings show a fundamental connection between white matter microstructure and neural synchronization that may be critical for cognitive processing. In the future, longitudinal or interventional studies can build upon our knowledge of these exciting relations between white matter, neural communication, and cognition.

Modulation of Cortical Oscillations by Low-Frequency Direct Cortical Stimulation Is State-Dependent.

Cortical oscillations play a fundamental role in organizing large-scale functional brain networks. Noninvasive brain stimulation with temporally patterned waveforms such as repetitive transcranial magnetic stimulation (rTMS) and transcranial alternating current stimulation (tACS) have been proposed to modulate these oscillations. Thus, these stimulation modalities represent promising new approaches for the treatment of psychiatric illnesses in which these oscillations are impaired. However, the mechanism by which periodic brain stimulation alters endogenous oscillation dynamics is debated and appears to depend on brain state. Here, we demonstrate with a static model and a neural oscillator model that recurrent excitation in the thalamo-cortical circuit, together with recruitment of cortico-cortical connections, can explain the enhancement of oscillations by brain stimulation as a function of brain state. We then performed concurrent invasive recording and stimulation of the human cortical surface to elucidate the response of cortical oscillations to periodic stimulation and support the findings from the computational models. We found that (1) stimulation enhanced the targeted oscillation power, (2) this enhancement outlasted stimulation, and (3) the effect of stimulation depended on behavioral state. Together, our results show successful target engagement of oscillations by periodic brain stimulation and highlight the role of nonlinear interaction between endogenous network oscillations and stimulation. These mechanistic insights will contribute to the design of adaptive, more targeted stimulation paradigms.

Decorrelated Input Dissociates Narrow Band γ Power and BOLD in Human Visual Cortex.

Although fMRI using the BOLD contrast is widely used for noninvasively mapping hemodynamic brain activity in humans, its exact link to underlying neural processing is poorly understood. Whereas some studies have reported that BOLD signals measured in visual cortex are tightly linked to neural activity in the narrow band γ (NBG) range, others have found a weak correlation between the two. To elucidate the mechanisms behind these conflicting findings, we hypothesized that BOLD reflects the strength of synaptic inputs to cortex, whereas NBG is more dependent on how well these inputs are correlated. To test this, we measured NBG, BOLD, and cerebral blood flow responses to stimuli that either correlate or decorrelate neural activity in human visual cortex. Next, we simulated a recurrent network model of excitatory and inhibitory neurons that reproduced in detail the experimental NBG and BOLD data. Results show that the visually evoked BOLD response was solely predicted by the sum of local inputs, whereas NBG was critically dependent on how well these inputs were correlated. In summary, the NBG-BOLD relationship strongly depends on the nature of sensory input to cortex: stimuli that increase the number of correlated inputs to visual cortex will increase NBG and BOLD in a similar manner, whereas stimuli that increase the number of decorrelated inputs will dissociate the two. The NBG-BOLD relationship is therefore not fixed but is rather highly dependent on input correlations that are both stimulus- and state-dependent.SIGNIFICANCE STATEMENT It is widely believed that γ oscillations in cortex are tightly linked to local hemodynamic activity. Here, we present experimental evidence showing how a stimulus can increase local blood flow to the brain despite suppressing γ power. Moreover, using a sophisticated model of cortical neurons, it is proposed that this occurs when synaptic input to cortex is strong yet decorrelated. Because input correlations are largely determined by the state of the brain, our results demonstrate that the relationship between γ and local hemodynamics is not fixed, but rather context dependent. This likely explains why certain neurodevelopmental disorders are characterized by weak γ activity despite showing normal blood flow.

Changes in White Matter Microstructure Impact Cognition by Disrupting the Ability of Neural Assemblies to Synchronize.

Cognition is compromised by white matter (WM) injury but the neurophysiological alterations linking them remain unclear. We hypothesized that reduced neural synchronization caused by disruption of neural signal propagation is involved. To test this, we evaluated group differences in: diffusion tensor WM microstructure measures within the optic radiations, primary visual area (V1), and cuneus; neural phase synchrony to a visual attention cue during visual-motor task; and reaction time to a response cue during the same task between 26 pediatric patients (17/9: male/female) treated with cranial radiation treatment for a brain tumor (12.67 ± 2.76 years), and 26 healthy children (16/10: male/female; 12.01 ± 3.9 years). We corroborated our findings using a corticocortical computational model representing perturbed signal conduction from myelin. Patients show delayed reaction time, WM compromise, and reduced phase synchrony during visual attention compared with healthy children. Notably, using partial least-squares-path modeling we found that WM insult within the optic radiations, V1, and cuneus is a strong predictor of the slower reaction times via disruption of neural synchrony in visual cortex. Observed changes in synchronization were reproduced in a computational model of WM injury. These findings provide new evidence linking cognition with WM via the reliance of neural synchronization on propagation of neural signals.SIGNIFICANCE STATEMENT By comparing brain tumor patients to healthy children, we establish that changes in the microstructure of the optic radiations and neural synchrony during visual attention predict reaction time. Furthermore, by testing the directionality of these links through statistical modeling and verifying our findings with computational modeling, we infer a causal relationship, namely that changes in white matter microstructure impact cognition in part by disturbing the ability of neural assemblies to synchronize. Together, our human imaging data and computer simulations show a fundamental connection between WM microstructure and neural synchronization that is critical for cognitive processing.

Suppression of underlying neuronal fluctuations mediates EEG slowing during general anaesthesia.

The physiological mechanisms by which anaesthetic drugs modulate oscillatory brain activity remain poorly understood. Combining human data, mathematical and computational analysis of both spiking and mean-field models, we investigated the spectral dynamics of encephalographic (EEG) beta-alpha oscillations, observed in human patients undergoing general anaesthesia. The effect of anaesthetics can be modelled as a reduction of neural fluctuation intensity, and/or an increase in inhibitory synaptic gain in the thalamo-cortical circuit. Unlike previous work, which suggested the primary importance of gamma-amino-butryic-acid (GABA) augmentation in causing a shift to low EEG frequencies, our analysis demonstrates that a non-linear transition, triggered by a simple decrease in neural fluctuation intensity, is sufficient to explain the clinically-observed appearance - and subsequent slowing - of the beta-alpha narrowband EEG peak. In our model, increased synaptic inhibition alone, did not correlate with the clinically-observed encephalographic spectral changes, but did cause the anaesthetic-induced decrease in neuronal firing rate. Taken together, our results show that such a non-linear transition results in functional fragmentation of cortical and thalamic populations; highly correlated intra-population dynamics triggered by anaesthesia decouple and isolate neural populations. Our results are able to parsimoniously unify and replicate the observed anaesthetic effects on both the EEG spectra and inter-regional connectivity, and further highlight the importance of neural activity fluctuations in the genesis of altered brain states.

Shaping Intrinsic Neural Oscillations with Periodic Stimulation.

UNLABELLED: Rhythmic brain activity plays an important role in neural processing and behavior. Features of these oscillations, including amplitude, phase, and spectrum, can be influenced by internal states (e.g., shifts in arousal, attention or cognitive ability) or external stimulation. Electromagnetic stimulation techniques such as transcranial magnetic stimulation, transcranial direct current stimulation, and transcranial alternating current stimulation are used increasingly in both research and clinical settings. Currently, the mechanisms whereby time-dependent external stimuli influence population-scale oscillations remain poorly understood. Here, we provide computational insights regarding the mapping between periodic pulsatile stimulation parameters such as amplitude and frequency and the response dynamics of recurrent, nonlinear spiking neural networks. Using a cortical model built of excitatory and inhibitory neurons, we explored a wide range of stimulation intensities and frequencies systematically. Our results suggest that rhythmic stimulation can form the basis of a control paradigm in which one can manipulate the intrinsic oscillatory properties of driven networks via a plurality of input-driven mechanisms. Our results show that, in addition to resonance and entrainment, nonlinear acceleration is involved in shaping the rhythmic response of our modeled network. Such nonlinear acceleration of spontaneous and synchronous oscillatory activity in a neural network occurs in regimes of intense, high-frequency rhythmic stimulation. These results open new perspectives on the manipulation of synchronous neural activity for basic and clinical research. SIGNIFICANCE STATEMENT: Oscillatory activity is widely recognized as a core mechanism for information transmission within and between brain circuits. Noninvasive stimulation methods can shape this activity, something that is increasingly capitalized upon in basic research and clinical practice. Here, we provide computational insights on the mechanistic bases for such effects. Our results show that rhythmic stimulation forms the basis of a control paradigm in which one can manipulate the intrinsic oscillatory properties of driven networks via a plurality of input-driven mechanisms. In addition to resonance and entrainment, nonlinear acceleration is involved in shaping the rhythmic response of our modeled network, particularly in regimes of high-frequency rhythmic stimulation. These results open new perspectives on the manipulation of synchronous neural activity for basic and clinical research.

Stimulus statistics shape oscillations in nonlinear recurrent neural networks.

Rhythmic activity plays a central role in neural computations and brain functions ranging from homeostasis to attention, as well as in neurological and neuropsychiatric disorders. Despite this pervasiveness, little is known about the mechanisms whereby the frequency and power of oscillatory activity are modulated, and how they reflect the inputs received by neurons. Numerous studies have reported input-dependent fluctuations in peak frequency and power (as well as couplings across these features). However, it remains unresolved what mediates these spectral shifts among neural populations. Extending previous findings regarding stochastic nonlinear systems and experimental observations, we provide analytical insights regarding oscillatory responses of neural populations to stimulation from either endogenous or exogenous origins. Using a deceptively simple yet sparse and randomly connected network of neurons, we show how spiking inputs can reliably modulate the peak frequency and power expressed by synchronous neural populations without any changes in circuitry. Our results reveal that a generic, non-nonlinear and input-induced mechanism can robustly mediate these spectral fluctuations, and thus provide a framework in which inputs to the neurons bidirectionally regulate both the frequency and power expressed by synchronous populations. Theoretical and computational analysis of the ensuing spectral fluctuations was found to reflect the underlying dynamics of the input stimuli driving the neurons. Our results provide insights regarding a generic mechanism supporting spectral transitions observed across cortical networks and spanning multiple frequency bands.

Cue-dependent circuits for illusory contours in humans.

Objects' borders are readily perceived despite absent contrast gradients, e.g. due to poor lighting or occlusion. In humans, a visual evoked potential (VEP) correlate of illusory contour (IC) sensitivity, the "IC effect", has been identified with an onset at ~90 ms and generators within bilateral lateral occipital cortices (LOC). The IC effect is observed across a wide range of stimulus parameters, though until now it always involved high-contrast achromatic stimuli. Whether IC perception and its brain mechanisms differ as a function of the type of stimulus cue remains unknown. Resolving such will provide insights on whether there is a unique or multiple solutions to how the brain binds together spatially fractionated information into a cohesive perception. Here, participants discriminated IC from no-contour (NC) control stimuli that were either comprised of low-contrast achromatic stimuli or instead isoluminant chromatic contrast stimuli (presumably biasing processing to the magnocellular and parvocellular pathways, respectively) on separate blocks of trials. Behavioural analyses revealed that ICs were readily perceived independently of the stimulus cue--i.e. when defined by either chromatic or luminance contrast. VEPs were analysed within an electrical neuroimaging framework and revealed a generally similar timing of IC effects across both stimulus contrasts (i.e. at ~90 ms). Additionally, an overall phase shift of the VEP on the order of ~30 ms was consistently observed in response to chromatic vs. luminance contrast independently of the presence/absence of ICs. Critically, topographic differences in the IC effect were observed over the ~110-160 ms period; different configurations of intracranial sources contributed to IC sensitivity as a function of stimulus contrast. Distributed source estimations localized these differences to LOC as well as V1/V2. The present data expand current models by demonstrating the existence of multiple, cue-dependent circuits in the brain for generating perceptions of illusory contours.

Distinctive biophysical features of human cell-types: insights from studies of neurosurgically resected brain tissue.

Electrophysiological characterization of live human tissue from epilepsy patients has been performed for many decades. Although initially these studies sought to understand the biophysical and synaptic changes associated with human epilepsy, recently, it has become the mainstay for exploring the distinctive biophysical and synaptic features of human cell-types. Both epochs of these human cellular electrophysiological explorations have faced criticism. Early studies revealed that cortical pyramidal neurons obtained from individuals with epilepsy appeared to function "normally" in comparison to neurons from non-epilepsy controls or neurons from other species and thus there was little to gain from the study of human neurons from epilepsy patients. On the other hand, contemporary studies are often questioned for the "normalcy" of the recorded neurons since they are derived from epilepsy patients. In this review, we discuss our current understanding of the distinct biophysical features of human cortical neurons and glia obtained from tissue removed from patients with epilepsy and tumors. We then explore the concept of within cell-type diversity and its loss (i.e., "neural homogenization"). We introduce neural homogenization to help reconcile the epileptogenicity of seemingly "normal" human cortical cells and circuits. We propose that there should be continued efforts to study cortical tissue from epilepsy patients in the quest to understand what makes human cell-types "human".

Reduced dynamics for delayed systems with harmonic or stochastic forcing.

The analysis of nonlinear delay-differential equations (DDEs) subjected to external forcing is difficult due to the infinite dimensionality of the space in which they evolve. To simplify the analysis of such systems, the present work develops a non-homogeneous center manifold (CM) reduction scheme, which allows the derivation of a time-dependent order parameter equation in finite dimension. This differential equation captures the major dynamical features of the delayed system. The forcing is assumed to be small compared to the amplitude of the autonomous system, in order to cause only small variations of the fixed points and of the autonomous CM. The time-dependent CM is shown to satisfy a non-homogeneous partial differential equation. We first briefly review CM theory for DDEs. Then we show, for the general scalar case, how an ansatz that separates the CM into one for the autonomous problem plus an additional time-dependent order-two correction leads to satisfying results. The paper then details the application to a transcritical bifurcation subjected to single or multiple periodic forcings. The validity limits of the reduction scheme are also highlighted. Finally, we characterize the specific case of additive stochastic driving of the transcritical bifurcation, where additive white noise shifts the mode of the probability density function of the state variable to larger amplitudes.

Homeostatic coordination and up-regulation of neural activity by activity-dependent myelination.

Activity-dependent myelination (ADM) is a fundamental dimension of brain plasticity through which myelin changes as a function of neural activity. Mediated by structural changes in glia, ADM notably regulates axonal conduction velocity. Yet, it remains unclear how neural activity impacts myelination to orchestrate the timing of neural signalling, and how ADM shapes neural activity. We developed a model of spiking neurons enhanced with neuron-oligodendrocyte feedback and examined the relationship between ADM and neural activity. We found that ADM implements a homeostatic gain control mechanism that enhances neural firing rates and correlations through the temporal coordination of action potentials as axon lengths increase. Stimuli engage ADM plasticity to trigger bidirectional and reversible changes in conduction delays, as may occur during learning. Furthermore, ADM was found to enhance information transmission under various types of time-varying stimuli. These results highlight the role of ADM in shaping neural activity and communication.

Loss of neuronal heterogeneity in epileptogenic human tissue impairs network resilience to sudden changes in synchrony.

A myriad of pathological changes associated with epilepsy can be recast as decreases in cell and circuit heterogeneity. We thus propose recontextualizing epileptogenesis as a process where reduction in cellular heterogeneity, in part, renders neural circuits less resilient to seizure. By comparing patch clamp recordings from human layer 5 (L5) cortical pyramidal neurons from epileptogenic and non-epileptogenic tissue, we demonstrate significantly decreased biophysical heterogeneity in seizure-generating areas. Implemented computationally, this renders model neural circuits prone to sudden transitions into synchronous states with increased firing activity, paralleling ictogenesis. This computational work also explains the surprising finding of significantly decreased excitability in the population-activation functions of neurons from epileptogenic tissue. Finally, mathematical analyses reveal a bifurcation structure arising only with low heterogeneity and associated with seizure-like dynamics. Taken together, this work provides experimental, computational, and mathematical support for the theory that ictogenic dynamics accompany a reduction in biophysical heterogeneity.

Neural adaptation facilitates oscillatory responses to static inputs in a recurrent network of ON and OFF cells.

We investigate the role of adaptation in a neural field model, composed of ON and OFF cells, with delayed all-to-all recurrent connections. As external spatially profiled inputs drive the network, ON cells receive inputs directly, while OFF cells receive an inverted image of the original signals. Via global and delayed inhibitory connections, these signals can cause the system to enter states of sustained oscillatory activity. We perform a bifurcation analysis of our model to elucidate how neural adaptation influences the ability of the network to exhibit oscillatory activity. We show that slow adaptation encourages input-induced rhythmic states by decreasing the Andronov-Hopf bifurcation threshold. We further determine how the feedback and adaptation together shape the resonant properties of the ON and OFF cell network and how this affects the response to time-periodic input. By introducing an additional frequency in the system, adaptation alters the resonance frequency by shifting the peaks where the response is maximal. We support these results with numerical experiments of the neural field model. Although developed in the context of the circuitry of the electric sense, these results are applicable to any network of spontaneously firing cells with global inhibitory feedback to themselves, in which a fraction of these cells receive external input directly, while the remaining ones receive an inverted version of this input via feedforward di-synaptic inhibition. Thus the results are relevant beyond the many sensory systems where ON and OFF cells are usually identified, and provide the backbone for understanding dynamical network effects of lateral connections and various forms of ON/OFF responses.

Responses of recurrent nets of asymmetric ON and OFF cells.

A neural field model of ON and OFF cells with all-to-all inhibitory feedback is investigated. External spatiotemporal stimuli drive the ON and OFF cells with, respectively, direct and inverted polarity. The dynamic differences between networks built of ON and OFF cells ("ON/OFF") and those having only ON cells ("ON/ON") are described for the general case where ON and OFF cells can have different spontaneous firing rates; this asymmetric case is generic. Neural responses to nonhomogeneous static and time-periodic inputs are analyzed in regimes close to and away from self-oscillation. Static stimuli can cause oscillatory behavior for certain asymmetry levels. Time-periodic stimuli expose dynamical differences between ON/OFF and ON/ON nets. Outside the stimulated region, we show that ON/OFF nets exhibit frequency doubling, while ON/ON nets cannot. On the other hand, ON/ON networks show antiphase responses between stimulated and unstimulated regions, an effect that does not rely on specific receptive field circuitry. An analysis of the resonance properties of both net types reveals that ON/OFF nets exhibit larger response amplitude. Numerical simulations of the neural field models agree with theoretical predictions for localized static and time-periodic forcing. This is also the case for simulations of a network of noisy integrate-and-fire neurons. We finally discuss the application of the model to the electrosensory system and to frequency-doubling effects in retina.