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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., (© 2024 Author(s). Published under an exclusive license by AIP Publishing.)

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., (© 2024 Author(s). Published under an exclusive license by AIP Publishing.)

We explore the emergence of a variety of different spatiotemporal patterns in a 2D lattice of self-sustained oscillators, which interact nonlocally through an active nonlinear element. A basic element is a van der Pol oscillator in a regime of relaxation oscillations. The active nonlinear coupling can be implemented by a radiophysical element with negative resistance in its current-voltage curve taking into account nonlinear characteristics (for example, a tunnel diode). We show that such coupling consists of two parts, namely, a repulsive linear term and an attractive nonlinear term. This interaction leads to the emergence of only standing waves with periodic dynamics in time and absence of any propagating wave processes. At the same time, many different spatiotemporal patterns occur when the coupling parameters are varied, namely, regular and complex cluster structures, such as chimera states. This effect is associated with the appearance of new periodic states of individual oscillators by the repulsive part of coupling, while the attractive term attenuates this effect. We also show influence of the coupling nonlinearity on the spatiotemporal dynamics.

We explore numerically the synchronization effects in a heterogeneous two-layer network of two-dimensional (2D) lattices of van der Pol oscillators. The inter-layer coupling of the multiplex network has an attractive character. One layer of 2D lattices is characterized by attractive coupling of oscillators and demonstrates a spiral wave regime for both local and nonlocal interactions. The oscillators in the second layer are coupled through active elements and the interaction between them has repulsive character. We show that the lattice with the repulsive type of coupling demonstrates complex spatiotemporal cluster structures, which can be called labyrinth-like structures. We show for the first time that this multiplex network with fundamentally various types of intra-layer coupling demonstrates mutual synchronization and a competition between two types of structures. Our numerical study indicates that the synchronization threshold and the type of spatiotemporal patterns in both layers strongly depend on the ratio of the intra-layer coupling strength of the two lattices. We also analyze the impact of intra-layer coupling ranges on the synchronization effects.

We study the synchronization of spatio-temporal patterns in a two-layer network of coupled chaotic maps, where each layer is represented by a nonlocally coupled ring. In particular, we focus on noisy inter-layer communication that we call multiplexing noise. We show that noisy modulation of inter-layer coupling strength has a significant impact on the dynamics of the network and specifically on the degree of synchronization of spatio-temporal patterns of interacting layers initially (in the absence of interaction) exhibiting chimera states. Our goal is to develop control strategies based on multiplexing noise for both identical and non-identical layers. We find that for the appropriate choice of intensity and frequency characteristics of parametric noise, complete or partial synchronization of the layers can be observed. Interestingly, for achieving inter-layer synchronization through multiplexing noise, it is crucial to have colored noise with intermediate spectral width. In the limit of white noise, the synchronization is destroyed. These results are the first step toward understanding the role of noisy inter-layer communication for the dynamics of multilayer networks.

We study numerically forced synchronization of a heterogeneous multilayer network in the regime of a complex spatiotemporal pattern. Retranslating the master chimera structure in a driving layer along subsequent layers is considered, and the peculiarities of forced synchronization are studied depending on the nature and degree of heterogeneity of the network, as well as on the degree of asymmetry of the inter-layer coupling. We also analyze the possibility of synchronizing all the network layers with a given accuracy when the coupling parameters are varied.

Using the model of a generalized Van der Pol oscillator in the regime of subcritical Hopf bifurcation, we investigate the influence of time delay on noise-induced oscillations. It is shown that for appropriate choices of time delay, either suppression or enhancement of coherence resonance can be achieved. Analytical calculations are combined with numerical simulations and experiments on an electronic circuit.

The dynamical structure of genetic networks determines the occurrence of various biological mechanisms, such as cellular differentiation. However, the question of how cellular diversity evolves in relation to the inherent stochasticity and intercellular communication remains still to be understood. Here, we define a concept of stochastic bifurcations suitable to investigate the dynamical structure of genetic networks, and show that under stochastic influence, the expression of given proteins of interest is defined via the probability distribution of the phase variable, representing one of the genes constituting the system. Moreover, we show that under changing stochastic conditions, the probabilities of expressing certain concentration values are different, leading to different functionality of the cells, and thus to differentiation of the cells in the various types.

We investigate the influence of additive Gaussian white noise on two different bistable self-sustained oscillators: Duffing-Van der Pol oscillator with hard excitation and a model of a synthetic genetic oscillator. In the deterministic case, both oscillators are characterized with a coexistence of a stable limit cycle and a stable equilibrium state. We find that under the influence of noise, their dynamics can be well characterized through the concept of stochastic bifurcation, consisting in a qualitative change of the stationary amplitude distribution. For the Duffing-Van der Pol oscillator analytical results, obtained for a quasiharmonic approach, are compared with the result of direct computer simulations. In particular, we show that the dynamics is different for isochronous and anisochronous systems. Moreover, we find that the increase of noise intensity in the isochronous regime leads to a narrowing of the spectral line. This effect is similar to coherence resonance. However, in the case of anisochronous systems, this effect breaks down and a new phenomenon, anisochronous-based stochastic bifurcation occurs.

We study the influence of external noise on the relaxation to an invariant probability measure for two types of nonhyperbolic chaotic attractors, a spiral (or coherent) and a noncoherent one. We find that for the coherent attractor the rate of mixing changes under the influence of noise, although the largest Lyapunov exponent remains almost unchanged. A mechanism of the noise influence on mixing is presented which is associated with the dynamics of the instantaneous phase of chaotic trajectories. This also explains why the noncoherent regime is robust against the presence of external noise.

We study numerically the effects of noise and periodic forcings on cluster synchronization in a chain of Van der Pol oscillators. We generalize the notion of effective synchronization to the case of a spatially extended system. It is shown that the structure of synchronized clusters can be effectively controlled by applying local external forcings. The effect of amplitude relations on the phase dynamics is also explored.

Lag synchronization denotes a particular form of synchronization in which the amplitudes of two interacting, nonidentical chaotic oscillators are correlated but there is a characteristic time delay between them. We study transitions to and between different forms of synchronization for the attractors defined as "in-phase" and "out-of-phase" and investigate the processes by which lag synchronization is lost in two coupled Rössler systems. With a small frequency mismatch between the two systems, these processes are related to the occurrence of a peculiar form of basin structure as more and more periodic orbits embedded into the synchronized chaotic state become unstable in a transverse direction.

In this paper we describe the transition to phase synchronization for systems of coupled nonlinear oscillators that individually follow the Feigenbaum route to chaos. A nested structure of phase synchronized regions of different attractor families is observed. With this structure, the transition to nonsynchronous behavior is determined by the loss of stability for the most stable synchronous mode. It is shown that the appearance of hyperchaos and the transition from lag synchronization to phase synchronization are related to the merging of chaotic attractors from different families. Numerical examples using Rossler systems and model maps are given. (c) 1999 American Institute of Physics.