Synchronization holds a significant role, notably within chaotic systems, in various contexts where the coordinated behavior of systems plays a pivotal and indispensable role. Hence, many studies have been dedicated to investigating the underlying mechanism of synchronization of chaotic systems. Networks with time-varying coupling, particularly those with blinking coupling, have been proven essential. The reason is that such coupling schemes introduce dynamic variations that enhance adaptability and robustness, making them applicable in various real-world scenarios. This paper introduces a novel adaptive blinking coupling, wherein the coupling adapts dynamically based on the most influential variable exhibiting the most significant average disparity. To ensure an equitable selection of the most effective coupling at each time instance, the average difference of each variable is normalized to the synchronous solution's range. Due to this adaptive coupling selection, synchronization enhancement is expected to be observed. This hypothesis is assessed within networks of identical systems, encompassing Lorenz, Rössler, Chen, Hindmarsh-Rose, forced Duffing, and forced van der Pol systems. The results demonstrated a substantial improvement in synchronization when employing adaptive blinking coupling, particularly when applying the normalization process.
Simplicial complexes are mathematical constructions that describe higher-order interactions within the interconnecting elements of a network. Such higher-order interactions become increasingly significant in neuronal networks since biological backgrounds and previous outcomes back them. In light of this, the current research explores a higher-order network of the memristive Rulkov model. To that end, the master stability functions are used to evaluate the synchronization of a network with pure pairwise hybrid (electrical and chemical) synapses alongside a network with two-node electrical and multi-node chemical connections. The findings provide good insight into the impact of incorporating higher-order interaction in a network. Compared to two-node chemical synapses, higher-order interactions adjust the synchronization patterns to lower multi-node chemical coupling parameter values. Furthermore, the effect of altering higher-order coupling parameter value on the dynamics of neurons in the synchronization state is researched. It is also shown how increasing network size can enhance synchronization by lowering the value of coupling parameters whereby synchronization occurs. Except for complete synchronization, cluster synchronization is detected for higher electrical coupling strength values wherein the neurons are out of the completed synchronization state.
Synchronization of interconnecting units is one of the hottest topics many researchers are interested in. In addition, this emerging phenomenon is responsible for many biological processes, and thus, the synchronization of interacting neurons is an important field of study in neuroscience. Employing the memristive Chialvo (mChialvo) neuron map, this paper investigates the effect of electrical, inner-linking, chemical, and hybrid coupling functions on the synchronization state of a neuronal network with regular structure. Master stability function (MSF) analysis is performed to obtain the necessary conditions for synchronizing the built networks. Afterward, the MSF-based results are confirmed by calculating the synchronization error. Besides, the dynamics of the synchronous neurons are discussed based on the bifurcation analysis. Our results suggest that, compared to the electrical and inner-linking functions, chemical synapses facilitate mChialvo neurons' synchronization since the neurons can achieve synchrony with a negligible chemical coupling strength. Further studies reveal that based on the active synapses, coupled mChialvo neurons can reach cluster synchronization, chimera state, sine-like synchronization, phase synchronization, and cluster phase synchronization.
One of the famous economic models in game theory is the duopoly Stackelberg model, in which a leader and a follower firm manufacture a single product in the market. Their goal is to obtain the maximum profit while competing with each other. The desired dynamics for a firm in a market is the convergence to its Nash equilibrium, but the dynamics of real-world markets are not always steady and can result in unpredictable market changes that exhibit chaotic behaviors. On the other hand, to approach reality more, the two firms in the market can be considered heterogeneous. The leader firm is bounded rationale, and the follower firm is adaptable. Modifying the cost function that affects the firms' profit by adding the marginal cost term is another step toward reality. We propose a Stackelberg model with heterogeneous players and marginal costs, which exhibits chaotic behavior. This model's equilibrium points, including the Nash equilibrium, are calculated by the backward induction method, and their stability analyses are obtained. The influence of changing each model parameter on the consequent dynamics is investigated through one-dimensional and two-dimensional bifurcation diagrams, Lyapunov exponents spectra, and Kaplan-Yorke dimension. Eventually, using a combination of state feedback and parameter adjustment methods, the chaotic solutions of the model are successfully tamed, and the model converges to its Nash equilibrium.
Non-alcoholic Fatty Liver Disease , Humans , Commerce , Game Theory , Models, Economic , Algorithms
Neural signatures of working memory have been frequently identified in the spiking activity of different brain areas. However, some studies reported no memory-related change in the spiking activity of the middle temporal (MT) area in the visual cortex. However, recently it was shown that the content of working memory is reflected as an increase in the dimensionality of the average spiking activity of the MT neurons. This study aimed to find the features that can reveal memory-related changes with the help of machine-learning algorithms. In this regard, different linear and nonlinear features were obtained from the neuronal spiking activity during the presence and absence of working memory. To select the optimum features, the Genetic algorithm, Particle Swarm Optimization, and Ant Colony Optimization methods were employed. The classification was performed using the Support Vector Machine (SVM) and the K-Nearest Neighbor (KNN) classifiers. Our results suggest that the deployment of spatial working memory can be perfectly detected from spiking patterns of MT neurons with an accuracy of 99.65±0.12 using the KNN and 99.50±0.26 using the SVM classifiers.
Algorithms , Memory, Short-Term , Machine Learning , Support Vector Machine , Neurons
Working memory has been identified as a top-down modulation of the average spiking activity in different brain parts. However, such modification has not yet been reported in the middle temporal (MT) cortex. A recent study showed that the dimensionality of the spiking activity of MT neurons increases after deployment of spatial working memory. This study is devoted to analyzing the ability of nonlinear and classical features to capture the content of the working memory from the spiking activity of MT neurons. The results suggest that only the Higuchi fractal dimension can be considered as a unique indicator of working memory while the Margaos-Sun fractal dimension, Shannon entropy, corrected conditional entropy, and skewness are perhaps indicators of other cognitive factors such as vigilance, awareness, and arousal as well as working memory.
Memory, Short-Term , Visual Cortex , Memory, Short-Term/physiology , Fractals , Neurons/physiology , Brain , Visual Cortex/physiology
We revisit the laser model with cavity loss modulation, from which evidence of chaos and generalized multistability was discovered in 1982. Multistability refers to the coexistence of two or more attractors in nonlinear dynamical systems. Despite its relative simplicity, the adopted model shows us how the multistability depends on the dissipation of the system. The model is then tested under the action of a secondary sinusoidal perturbation, which can remove bistability when a suitable relative phase is chosen. The surviving attractor is the one with less dissipation. This control strategy is particularly useful when one of the competing attractors is a chaotic attractor.
Higher-order interactions might play a significant role in the collective dynamics of the brain. With this motivation, we here consider a simplicial complex of neurons, in particular, studying the effects of pairwise and three-body interactions on the emergence of synchronization. We assume pairwise interactions to be mediated through electrical synapses, while for second-order interactions, we separately study diffusive coupling and nonlinear chemical coupling. For all the considered cases, we derive the necessary conditions for synchronization by means of linear stability analysis, and we compute the synchronization errors numerically. Our research shows that the second-order interactions, even if of weak strength, can lead to synchronization under significantly lower first-order coupling strengths. Moreover, the overall synchronization cost is reduced due to the introduction of three-body interactions if compared to pairwise interactions.
Models, Neurological , Nerve Net , Brain , Cluster Analysis , Neurons
In neuronal network analysis on, for example, synchronization, it has been observed that the influence of interactions between pairwise nodes is essential. This paper further reveals that there exist higher-order interactions among multi-node simplicial complexes. Using a neuronal network of Rulkov maps, the impact of such higher-order interactions on network synchronization is simulated and analyzed. The results show that multi-node interactions can considerably enhance the Rulkov network synchronization, better than pairwise interactions, for involving more and more neurons in the network.
Models, Neurological , Neurons , Neurons/physiology
Map-based neuronal models have received much attention due to their high speed, efficiency, flexibility, and simplicity. Therefore, they are suitable for investigating different dynamical behaviors in neuronal networks, which is one of the recent hottest topics. Recently, the memristive version of the Rulkov model, known as the m-Rulkov model, has been introduced. This paper investigates the network of the memristive version of the Rulkov neuron map to study the effect of the memristor on collective behaviors. Firstly, two m-Rulkov neuronal models are coupled in different cases, through electrical synapses, chemical synapses, and both electrical and chemical synapses. The results show that two electrically coupled memristive neurons can become synchronous, while the previous studies have shown that two non-memristive Rulkov neurons do not synchronize when they are coupled electrically. In contrast, chemical coupling does not lead to synchronization; instead, two neurons reach the same resting state. However, the presence of both types of couplings results in synchronization. The same investigations are carried out for a network of 100 m-Rulkov models locating in a ring topology. Different firing patterns, such as synchronization, lagged-phase synchronization, amplitude death, non-stationary chimera state, and traveling chimera state, are observed for various electrical and chemical coupling strengths. Furthermore, the synchronization of neurons in the electrical coupling relies on the network's size and disappears with increasing the nodes number.
Models, Neurological , Nerve Net , Neurons
Mitral Valve Prolapse (MVP) is a common condition among people, which is often benign and does not need any serious treatment. However, this doesn't mean that MVP can't cause any problems. In malignant conditions, MVP can cause mitral failure and also heart failure. Early diagnosis of MVP is significantly important to control and reduce its complications. Since the phonocardiogram signal provides useful information about heart valves function, it can be used for MVP detection. To detect MVP, the signal was denoised and segmented into heart cycles and constant three-second pieces in the first and second approaches, respectively. Next, based on the Fractional Fourier Transform (FrFT), the desired features were extracted. Then, the extracted features were windowed by a Moving Logarithmic Median Window (MLMW) and optimum features were selected using Mahalanobis, Bhattacharyya, Canberra, and Minkowski distance criteria. Finally, using the selected features, classification was performed by using the K-Nearest Neighbor (KNN) and the Suppor Vector Machine (SVM) classifiers to find out whether a segment is prolapsed. The best results of the experiment on the collected database contain 15 prolapsed and 6 non-prolapsed subjects using the A-test method show 96.25 ± 2.43 accuracy, 98.5 ± 3.37 sensitivity, 94.0 ± 5.16 specificity, 96.0 ± 3.44 precision, 92.5 ± 4.86 kappa, and 96.6 ± 2.34 f-score with the SVM classifier.
Mitral Valve Prolapse , Fourier Analysis , Humans , Mitral Valve/diagnostic imaging , Mitral Valve/pathology , Mitral Valve Prolapse/diagnostic imaging , Mitral Valve Prolapse/pathology , Phonocardiography
