Nadezhda Semenova

Coherence-Resonance Chimeras in a Network of Excitable Elements.

We demonstrate that chimera behavior can be observed in nonlocally coupled networks of excitable systems in the presence of noise. This phenomenon is distinct from classical chimeras, which occur in deterministic oscillatory systems, and it combines temporal features of coherence resonance, i.e., the constructive role of noise, and spatial properties of chimera states, i.e., the coexistence of spatially coherent and incoherent domains in a network of identical elements. Coherence-resonance chimeras are associated with alternating switching of the location of coherent and incoherent domains, which might be relevant in neuronal networks.

Does hyperbolicity impede emergence of chimera states in networks of nonlocally coupled chaotic oscillators

We analyze nonlocally coupled networks of identical chaotic oscillators with either time-discrete or time-continuous dynamics (Henon map, Lozi map, Lorenz system). We hypothesize that chimera states, in which spatial domains of coherent (synchronous) and incoherent (desynchronized) dynamics coexist, can be obtained only in networks of oscillators with nonhyperbolic chaotic attractors and cannot be found in networks of systems with hyperbolic chaotic attractors. This hypothesis is supported by analytical results and numerical simulations for hyperbolic and nonhyperbolic cases.

Temporal intermittency and the lifetime of chimera states in ensembles of nonlocally coupled chaotic oscillators

We describe numerical results for the dynamics of networks of nonlocally coupled chaotic maps. Switchings in time between amplitude and phase chimera states have been first established and studied. It has been shown that in autonomous ensembles, a nonstationary regime of switchings has a finite lifetime and represents a transient process towards a stationary regime of phase chimera. The lifetime of the nonstationary switching regime can be increased to infinity by applying short-term noise perturbations.

“Coherence–incoherence” transition in ensembles of nonlocally coupled chaotic oscillators with nonhyperbolic and hyperbolic attractors

We consider in detail similarities and differences of the “coherence–incoherence” transition in ensembles of nonlocally coupled chaotic discrete-time systems with nonhyperbolic and hyperbolic attractors. As basic models we employ the Hénon map and the Lozi map. We show that phase and amplitude chimera states appear in a ring of coupled Hénon maps, while no chimeras are observed in an ensemble of coupled Lozi maps. In the latter, the transition to spatio-temporal chaos occurs via solitary states. We present numerical results for the coupling function which describes the impact of neighboring oscillators on each partial element of an ensemble with nonlocal coupling. Varying the coupling strength we analyze the evolution of the coupling function and discuss in detail its role in the “coherence–incoherence” transition in the ensembles of Hénon and Lozi maps.

New type of chimera and mutual synchronization of spatiotemporal structures in two coupled ensembles of nonlocally interacting chaotic maps

We study numerically the dynamics of a network made of two coupled one-dimensional ensembles of discrete-time systems. The first ensemble is represented by a ring of nonlocally coupled Henon maps and the second one by a ring of nonlocally coupled Lozi maps. We find that the network of coupled ensembles can realize all the spatio-temporal structures which are observed both in the Henon map ensemble and in the Lozi map ensemble while uncoupled. Moreover, we reveal a new type of spatiotemporal structure, a solitary state chimera, in the considered network. We also establish and describe the effect of mutual synchronization of various complex spatiotemporal patterns in the system of two coupled ensembles of Henon and Lozi maps.

Time-delayed feedback control of coherence resonance chimeras

Using the model of a FitzHugh-Nagumo system in the excitable regime, we investigate the influence of time-delayed feedback on noise-induced chimera states in a network with nonlocal coupling, i.e., coherence resonance chimeras. It is shown that time-delayed feedback allows for the control of the range of parameter values where these chimera states occur. Moreover, for the feedback delay close to the intrinsic period of the system, we find a novel regime which we call period-two coherence resonance chimera.

Noise-Induced Chimera States in a Neural Network

We show that chimera patterns can be induced by noise in nonlocally coupled neural networks in the excitable regime. In contrast to classical chimeras, occurring in noise-free oscillatory networks, they have features of two phenomena: coherence resonance and chimera states. Therefore, we call them coherence-resonance chimeras. These patterns demonstrate the constructive role of noise and appear for intermediate values of noise intensity, which is a characteristic feature of coherence resonance. In the coherence-resonance chimera state a neural network of identical elements splits into two coexisting domains with different behavior: spatially coherent and spatially incoherent, a typical property of chimera states. Moreover, these noise-induced chimera states are characterized by alternating behavior: coherent and incoherent domains switch periodically their location. We show that this alternating switching can be explained by analyzing the coupling functions.

Fibonacci stairs and the Afraimovich-Pesin dimension for a stroboscopic section of a nonautonomous van der Pol oscillator

Statistics of Poincaré recurrences is studied in the stroboscopic section of trajectories of a nonautonomous van der Pol oscillator in the framework of the global approach. It is shown that when the oscillator frequency and the frequency of the external force are irrationally related, the set obtained stroboscopically is equivalent to the circle map. For small values of the external amplitude, the Fibonacci stairs is constructed for the golden and silver ratios and its universal properties are confirmed. It is established that the Afraimovich-Pesin dimension for the map in the stroboscopic section is αc = 1 for Diophantine irrational rotation numbers.

Poincaré Recurrences in a Nonautonomous Chaotic Map

The statistics of Poincare recurrences is studied numerically in a one-dimensional cubic map in the presence of harmonic and noisy excitations. It is shown that the distribution density of Poincare recurrences is periodically modulated by the harmonic force. It is established that the relationship between the Afraimovich–Pesin dimension and Lyapunov exponents is violated in the nonautonomous system.

Poincaré Recurrences in Ergodic Systems Without Mixing

We study numerically the statistics of recurrences in ergodic sets of the circle map type by using the multifractality analysis . We consider the standard circle map as well as the sets generated in stroboscopic sections of phase trajectories in a nonautonomous van der Pol oscillator and in a harmonically driven conservative nonlinear oscillator . The universal properties of the recurrence time dependence on the size of a return region are established. The numerical results demonstrate a full correspondence with the theoretical data obtained by Valentin Afraimovich.