We investigate how stochastic Poisson impulsive forcing influences the spatiotemporal dynamics of a two-dimensional network of Hindmarsh-Rose neurons. Unlike continuous noise, impulsive forcing introduces discrete, state-dependent perturbations, making the system response highly sensitive to both the statistics and the spatial structure of the input. In most of the parameter space, stochastic impulses destabilize the initial coherent spiral-wave regime and lead to unstable spiral-wave activity. At the same time, they can also produce constructive effects. Both spatially uniform and spatially non-uniform forcing induce stable target waves that are absent in the autonomous system, suggesting a common mechanism of structure formation driven by discrete excitation events. In addition, spatially uniform forcing suppresses spatial heterogeneity and leads to coherent, nearly synchronous oscillations, demonstrating that even random impulses can promote global synchronization. By contrast, spatially uncorrelated forcing enhances front fragmentation and incoherence, especially at higher amplitudes. To identify and compare the resulting regimes in a highly multistable parameter space, we use a feature-based clustering approach based on statistical descriptors of wave morphology and evolution across multiple time scales. This results in a clear separation of physically distinct regimes. Overall, stochastic Poisson impulses serve not only as a source of disorder but also as an effective control mechanism for destabilizing, reorganizing, and synchronizing collective wave dynamics in networks of coupled neuronal oscillators.

We aim to explore the features of destroying the spiral wave regime in a lattice network of Chialvo neurons by applying external noise with different statistical characteristics. Chialvo neurons are represented with a two-dimensional recurrence map. The lattice of neurons under study observed with random initial conditions and with special initial conditions for local and nonlocal coupling. We consider a detailed two-parameter plot in the plane of coupling strength - distribution width of L & eacute;vy process which revealed that the existence of spiral waves are dependent on the network and noise parameters. We examine how coupling strength and range parameters influence on the spiral wave dynamics in a coupled lattice system. Increasing the coupling range enlarges the region where spiral waves can exist. Additionally we show that the destruction of spiral waves is achievable with a certain threshold of the distribution width parameter value depending on the noise stability parameter value and the noise asymmetry parameter value. A decrease in the noise stability parameter as well as in the noise asymmetry parameter decreases the threshold value. We show that the influence of L & eacute;vy noise on spiral waves in the lattice of Chialvo neurons results in a transition to target waves that are more stable than in the case of transition for random initial conditions to target waves without noise. Finally, we have found that the noise could cause the lattice to switch between various spiral-like regimes as time passes.

We study the effect of Levy noise on phase synchronization in adaptive ensembles of excitable elements. We consider an ensemble of FitzHugh-Nagumo neurons with nonlocal coupling and a ring topology, under the external additive alpha-stable Levy noise. A key feature of the model is the adaptive coupling tuning mechanism, which adjusts the strength of interactions between neurons based on a moving average of the interspike interval. The coupling strength increases during spikes with a large interspike interval and decreases during synchronous spikes, which allows the network to automatically adjust the minimum necessary total coupling strength to maintain a coherent regime even under strong noise with heavy distribution tails. We found that the coherent resonance characteristic of a single neuron is also observed in a coupled system. However, the optimal noise intensity shifts to lower values as the coupling range increases. Synchronization is achieved only at a certain coupling range, while at a lower coupling range only cluster synchronization is possible even with strong coupling of neurons. Levy noise requires a stronger global interaction between neurons to achieve synchronization compared to Gaussian noise. However, the positive asymmetry of the noise distribution significantly reduces this threshold due to the increased sensitivity of neurons to positive fluctuations. The proposed adaptive mechanism successfully ensures synchronization of the system in the entire studied range of Levy noise parameters and connection topology, demonstrating the versatility, high adaptation speed and energy efficiency of the approach. The obtained results open up new possibilities for controlled coordination of spatiotemporal dynamics in neural and other nonlinear excitable systems under extreme stochastic influences.

We demonstrate that nonlocal coupling enables control of the collective stochastic dynamics in the regime of coherence resonance. The control scheme based on the nonlocal interaction properties is presented by means of numerical simulation on an example of coupled FitzHugh-Nagumo oscillators. In particular, increasing the coupling radius is shown to enhance or to suppress the effect of coherence resonance, which is reflected in the evolution of the dependence of the correlation time and the deviation of interspike intervals on the noise intensity. Nonlocal coupling is considered an intermediate option between local and global coupling topologies, which are also discussed in the context of the coherence resonance control.

We investigate a spike activity of a network of excitable FitzHugh-Nagumo neurons, which is under constant two-frequency auditory signals. The neurons are supplemented with linear frequency filters and nonlinear input signal converters. We show that it is possible to configure the network to recognize a specific frequency ratio (musical interval) by selecting the parameters of the neurons, input filters, and coupling between neurons. A set of appropriately configured subnetworks with different topologies and coupling strengths can serve as a classifier for musical intervals. We have found that the selective properties of the classifier are due to the presence of a specific topology of coupling between the neurons of the network.

In this paper, we explore numerically the impact of different types of inter-layer coupling on the dynamics of a two-layer multiplex network of coupled FitzHugh–Nagumo oscillators in the excitable regime. For this purpose, the cases of attractive, repulsive, and periodically modulated inter-layer coupling are considered. Coupled in the ring structure, the FitzHugh–Nagumo neurons demonstrate travelling wave regimes which are different for the attractive and repulsive intra-layer coupling. It is shown that the inter-layer coupling affects not only the frequency of oscillations of individual neurons but also the spatio-temporal structures in individual layers in different ways, depending on the sign of the inter-layer coupling. It is established that complete in-phase synchronization of travelling waves is well achieved in the presence of attractive inter-layer coupling, while the repulsive inter-layer coupling induces effective anti-phase synchronization of wave regimes. When the inter-layer coupling is periodically modulated, the wave structures in both layers are distorted, and clusters of coherent and incoherent dynamics can appear in the ring space. The paper was presented at PhysCon2024.

We present numerical results on the effects of two presynaptic FitzHugh-Nagumo neurons on a postsynaptic neuron under unidirectional electrical coupling. The presynaptic neurons affect the postsynaptic neuron not simultaneously but with a certain time shift. We consider cases where the amplitudes of the presynaptic spikes can be both higher and lower than the excitation threshold level. The latter case receives the main attention in our work. We carefully examine the conditions under which the postsynaptic neuron is excited by the two asynchronous external spikes. With arbitrarily chosen parameters, the FitzHugh-Nagumo neuron is almost incapable of accumulating the energy of external signals, unlike, for example, the leaky integrate-and-fire neuron. In this case, the postsynaptic neuron only excites with a very short time delay between external impulses. However, we have discovered, for the first time, a parameter region where neuron excitation is possible even with significant time delays between presynaptic impulses with subthreshold amplitudes. We explain this effect in detail and describe the mechanism behind its occurrence. We identify the boundaries of this region in the parameter plane of time delay and coupling coefficient by varying the control parameter values of the neurons. The FitzHugh-Nagumo neuron has not previously been used as a node in spiking neural networks for training via spike-timing-dependent plasticity due to the lack of an integrate-and-fire effect. However, the detection of a certain range of parameters makes the potential application of this neuron for STDP training possible.

We study the spike activity of two mutually coupled FitzHugh – Nagumo neurons, which is influenced by two-frequency signals. The ratio of frequencies in the external signal corresponds to musical intervals (consonances). It has been discovered that this system can exhibit selective properties for identifying musical intervals. The mechanism of selectivity is shown, which is associated with the influence on the spiking frequency of neurons by intensity of the external signal and nature of the interaction of neurons.

We study numerically effects of time delay in networks of delay-coupled excitable FitzHugh-Nagumo systems with dissipation. Generation of periodic self-sustained oscillations and its threshold are analyzed depending on the dissipation of a single neuron, the delay time, and random initial conditions. The peculiarities of spatiotemporal dynamics of time-delayed bidirectional ring-structured FitzHugh-Nagumo neuronal systems are investigated in cases of local and nonlocal coupling topology between the nodes, and a first-order nonequilibrium phase transition to synchrony is established. It is shown that the emergence of an oscillatory activity in delay-coupled FitzHugh-Nagumo neurons is observed for smaller values of the coupling strength as the dissipation parameter decreases. This can provide the possibility of controlling the spatiotemporal behavior of the considered neuronal networks. The observed effects are quantified by plotting distributions of the maximal Lyapunov exponent and the global order parameter in terms of delay and coupling strength.

The stochastic FitzHugh-Nagumo model with time delayed-feedback is often studied in excitable regime to demonstrate the time-delayed control of coherence resonance. Here, we show that the impact of time-delayed feedback in the FitzHugh-Nagumo neuron is not limited by control of noise-induced oscillation regularity (coherence), but also results in excitation of the regular and chaotic self-oscillatory dynamics in the deterministic model. We demonstrate this numerically by means of simulations, linear stability analysis, the study of Lyapunov exponents and basins of attraction for both positive and negative delayed-feedback strengths. It has been established that one can implement a route to chaos in the explored model, where the intrinsic peculiarities of the Feigenbaum scenario are exhibited. For large time delay, we complement the study of temporal evolution by the interpretation of the dynamics as patterns in virtual space.

The work is devoted to the study of biology-relevant neural networks, which are called spiking neural networks (SNN), and is aimed at classifying two-frequency auditory signals. We consider an ensemble of FitzHugh-Nagumo neurons. Each neuron is connected to a radiophysical circuit tuned to a certain signal frequency. Different clusters of neurons respond to signals with different ratios of frequencies applied to all circuits simultaneously.

In this paper, we develop a new algorithm for estimating control parameter values of ordinary differential equation (ODE) models. We call it the complex error minimization algorithm with an adaptive rate of change. It efficiently determines the parameters of ODE models even over extremely short time series. The algorithm is based on the gradient method and successfully solves its major drawback, namely getting stuck in local minima. To detect the getting stuck, we first introduce the calculation of four different errors at once. Our studies show that they achieved the global minimum only when we observe simultaneous minimization of all these errors. When getting stuck in local minima takes place, only one (or several) errors are minimized, while the others remain unchanged or grow. Thus, the algorithm accurately detects getting stuck in local minima. After this, it applies special methods based on simulated annealing to escape from local minima. The algorithm selects the most optimal path for convergence of parameter values to the global minimum by applying random restarts and multi-start methods to avoid local minima. We have tested our method on models with regular and chaotic dynamics and have found that it can work with high accuracy in these cases. Our method is suitable for actual systems with complex dynamics and an extensive set of control parameters but short time series. Thus, the proposed algorithm is an effective method for solving the inverse problem of ODE models.

We study numerically the spatiotemporal dynamics and anti-phase synchronization of complex structures in a two-layer multiplex network of bidirectionally and repulsively coupled two-dimensional lattices. Each layer consists of locally and attractively coupled identical van der Pol oscillators. Depending on randomly distributed initial conditions the isolated layers can exhibit either a spiral or a target wave regime. The latter is found for first time for the locally coupled van der Pol lattice considered in this work. We vary the inter-layer coupling strength for either fixed or changing intra-layer coupling strengths in the interacting layers. The numerical results are summarized in the two-dimensional diagrams plotted in the "intra-layer coupling strength - inter-layer coupling strength " parameter plane. Anti-phase synchronization is identified by evaluating the local and global cross -correlation coefficients which are equal to-1. We also explore the impact of random de-multiplexing on the robustness of the observed spatiotemporal structures and anti-phase synchronized regimes in the two-layer network.

This paper considers the effects of forced and mutual synchronization of complex spatio-temporal structures in a two-layer network of nonlocally coupled logistic maps in the presence of inhomogeneous interlayer coupling. Two different types of coupling topology are considered: the first one is the sparse interlayer coupling with randomly distributed coupling defects, and the second type is the cluster interlayer coupling, providing the coupling via designated finite groups of elements. The latter type of coupling topology is considered for the first time. As a quantitative measure of the synchronization effect on the network, variance averaged over time and variance averaged both over time and network elements are used. We analyze how the synchronization measure changes depending on a degree of the interlayer coupling sparseness. We also identify a cluster of network elements which can provide almost complete synchronization in the network under study when the interlayer coupling is introduced along them.

We explore numerically relay synchronization of wave structures in a heterogeneous three-layer network of coupled two-dimensional (2D) lattices of continuous-time systems. Remote layers, which are not directly connected but interact via a relay layer, consist of coupled van der Pol oscillators, while the middle layer is described by a lattice of interacting FitzHugh-Nagumo neurons. We show for the first time that already for weak inter-layer coupling, anti-phase relay synchronization of target wave patterns occurs in the considered network. This is a novel effect which can be observed in multiplex networks of interacting 2D lattices of oscillatory systems. Our numerical studies indicate that strong inter-layer coupling leads to in-phase synchronization of spatio-coherent structures in the network layers. We also analyze the impact of inter-layer coupling ranges in the relay and the remote layers on the relay synchronization effect. (c) 2020 Elsevier Ltd. All rights reserved.

We describe spatiotemporal patterns in a network of identical van der Pol oscillators coupled in a two-dimensional geometry. In this study, we show that the system under study demonstrates a plethora of different spatiotemporal structures including chimera states when the coupling parameters are varied. Spiral wave chimeras are formed in the network when the coupling strength is rather large and the coupling range is short enough. Another type of chimeras is a target wave chimera. It is shown that solitary states play a crucial role in forming an incoherence cluster of this chimera state. They can also spread within the coherence cluster. Furthermore, when the coupling range increases, the target wave chimera evolves to the regime of solitary states which are randomly distributed in space. Growing the coupling strength leads to the attraction of solitary states to a certain spatial region, while the synchronous regime is set in the other part of the system. This spatiotemporal pattern represents a solitary state chimera, which is firstly found in the system of continuous-time oscillators. We offer the explanation of these phenomena and describe the evolution of the regimes in detail. (C) 2020 Elsevier Ltd. All rights reserved.

We analyse the synchronization of spatiotemporal patterns based on spiral and target waves, which are realized in a multiplex network consisting of two nonidentical 2D lattices of the nonlocally coupled van der Pol oscillators. We study the syncronization and its features for two types of the inter-layer unidirectional coupling, namely dissipative and inertial. We show that the synchronization features for these cases are significantly different. When the inter-layer coupling is dissipative the synchronization between the layers is observed only for the strong inter-layer coupling or is even impossible. For the case of inertial interaction the layers are synchronized at sufficiently weak coupling strength. At the same time, there are "desynchronization windows", in which the layer regimes are no longer synchronized. We explain these phenomena by a noticeably different influence of the inter-layer coupling on the dynamics of individual oscillators in the cases of dissipative and inertial interaction of the layers. (C) 2020 Elsevier B.V. All rights reserved.

In the present paper we study numerically the interaction of two 2-dimensional networks each representing a lattice of coupled van der Pol oscillators. The isolated lattices can demonstrate spiral and target wave structures for the cases of no-flux boundary conditions and random initial conditions. We explore the effect of mutual synchronization of target waves and target wave chimeras for dissipative and inertial inter-layer coupling between the lattices and for local and nonlocal intra-layer coupling between the lattice oscillators. We show for the first time the possibility of complete synchronization of target wave chimera states, including synchronization of incoherent cores. Our findings demonstrate that there is a difference with synchronization of spiral wave chimera states in which incoherent cores are not completely synchronized. The obtained results can have an important application and can be particularly used to study the dynamics of cardiac muscle in biophysics. (C) 2020 Elsevier Ltd. All rights reserved.

Backgrounds and Objectives: Networks of coupled dynamical o scillators are of high interest for last decades. The interest to their dynamics greatly increases with the discovery of chimera states. The latter are characterized by the coexistence of regions with coherent and incoherent behavior. There are many works devoted to the networks with nonlocal coupling topology, but the influence of the coupling topology type has not been sufficiently studied. In this paper we consider recently proposed reflecting and diagonal topologies of coupling and compare them with the nonlocal coupling. The issue addressed in the paper is of great interest and importance because of the topological correspondence to biological neuron networks. Logistic maps, FitzHugh-Nagumo oscillators, and Courbage-Nekorkin models are selected as partial subsystems in networks. Materials and Methods: The numerical analysis is carried out using a program complex in C++ which was developed for modeling dynamical systems with different topologies of coupling. Snapshots of amplitudes of oscillators and spatio-temporal diagrams are used to diagnose the dynamical regimes. Results: Numerical results have shown that a number of incoherent areas of chimera states varies when the coupling topology changes. In addition, the features of the transition from the incoherence regime to the completely synchronized state with increasing coupling strength depend on the choice of coupling topology. It is shown that a certain type of waves, namely, traveling waves, cannot be realized in the case of reflecting coupling. Conclusion: The performed studies have indicated that the coupling topology can affect the behavior of the networks. There is a possibility to obtain different regimes by choosing different topologies of coupling. Herewith, the coupling strength value for chimera states is preserved as the coupling topology changes.