Collective dynamics of a coupled Hindmarsh-Rose neurons with locally active memristor.

A Locally active memristors can mimic neural synapses, resulting in rich neuro-morphological dynamics in biological neurons. To illustrate the impact of a local active memristive synapse, we consider coupled Hindmarsh-Rose (HR) neurons. Firstly, the dynamical transitions of the proposed system are investigated using bifurcation analysis and Lyapunov exponents, and we find that the transition between periodic and chaotic states depends on the input currents and memristive coupling strength. By performing the two-parameter analysis, the existence of periodic and chaotic regions is revealed. The collective behavior is then examined by expanding the network to include memristive coupled HR neurons under different network connectivities. We show that the system achieves synchronization behavior for all network connectivities, including regular, random, and small-world, when the strength of the memristive coupling is increased.

Impact of external excitations on blinking enhanced synchronization in bistable vibrational energy harvesters.

Vibrational energy harvesters are capable of converting low-frequency broad-band mechanical energy into electrical power and can be used in implantable medical devices and wireless sensors. With the use of such energy harvesters, it is feasible to generate continuous power that is more reliable and cost-effective. According to previous findings, the energy harvester can offer rich complex dynamics, one of which is obtaining the synchronization behavior, which is intriguing to achieve desirable power from energy harvesters. Therefore, we consider bistable energy harvesters with periodic and quasiperiodic excitations to investigate synchronization. Specifically, we introduce blinking into the coupling function to check whether it improves the synchronization. Interestingly, we discover that raising the normalized proportion of blinking can initiate synchronization behaviors even with lower optimal coupling strength than the absence of blinking in the coupling (i.e., continuous coupling). The existence of synchronization behaviors is confirmed by finding the largest Lyapunov exponents. In addition, the results show that the optimal coupling strength needed to achieve synchronization for quasiperiodic excitations is smaller than that for periodic excitations.

Emergence of extreme events in a quasiperiodic oscillator.

Extreme events are unusual and rare large-amplitude fluctuations can occur unexpectedly in nonlinear dynamical systems. Events above the extreme event threshold of the probability distribution of a nonlinear process characterize extreme events. Different mechanisms for the generation of extreme events and their prediction measures have been reported in the literature. Based on the properties of extreme events, such as those that are rare in the frequency of occurrence and extreme in amplitude, various studies have shown that extreme events are both linear and nonlinear in nature. Interestingly, in this Letter, we report on a special class of extreme events which are nonchaotic and nonperiodic. These nonchaotic extreme events appear in between the quasiperiodic and chaotic dynamics of the system. We report the existence of such extreme events with various statistical measures and characterization techniques.

Bursting during intermittency route to thermoacoustic instability: Effects of slow-fast dynamics.

Intermittency observed prior to thermoacoustic instability is characterized by the occurrence of bursts of high-amplitude periodic oscillations (active state) amidst epochs of low-amplitude aperiodic fluctuations (rest state). Several model-based studies conjectured that bursting arises due to the underlying turbulence in the system. However, such intermittent bursts occur even in laminar and low-turbulence combustors, which cannot be explained by models based on turbulence. We assert that bursting in such combustors may arise due to the existence of subsystems with varying timescales of oscillations, thus forming slow-fast systems. Experiments were performed on a horizontal Rijke tube and the effect of slow-fast oscillations was studied by externally introducing low-frequency sinusoidal modulations in the control parameter. The induced bursts display an abrupt transition between the rest and the active states. The growth and decay patterns of such bursts show asymmetry due to delayed bifurcation caused by slow oscillations of the control parameter about the Hopf bifurcation point. Further, we develop a phenomenological model for the interaction between different subsystems of a thermoacoustic system by either coupling the slow and fast subsystems or by introducing noise in the absence of slow oscillations of the control parameter. We show that interaction between subsystems with different timescales leads to regular amplitude modulated bursting, while the presence of noise induces irregular amplitude modulations in the bursts. Thus, we speculate that bursting in laminar and low-turbulence systems occurs predominantly due to the interdependence between slow and fast oscillations, while bursting in high-turbulence systems is predominantly influenced by the underlying turbulence.