Tatiana E. Vadivasova

Correlation analysis of the coherence-incoherence transition in a ring of nonlocally coupled logistic maps

We present numerical results for a set of bifurcations occurring at the transition from complete chaotic synchronization to spatio-temporal chaos in a ring of nonlocally coupled chaotic logistic maps. The regularities are established for the evolution of cross-correlations of oscillations in the network elements at the bifurcations related to the coupling strength variation. We reveal the distinctive features of cross-correlations for phase and amplitude chimera states. It is also shown that the effect of time intermittency between the amplitude and phase chimeras can be realized in the considered ensemble.

Hard and soft excitation of oscillations in memristor-based oscillators with a line of equilibria

A model of memristor-based Chua’s oscillator is studied. The considered system has infinitely many equilibrium points, which build a line of equilibria. Bifurcational mechanisms of oscillation excitation are explored for different forms of nonlinearity. Hard and soft excitation scenarios have principally different nature. The hard excitation is determined by the memristor piecewise-smooth characteristic and is a result of a border-collision bifurcation. The soft excitation is caused by addition of a smooth nonlinear function and has distinctive features of the supercritical Andronov–Hopf bifurcation. Mechanisms of instability and amplitude limitation are described for both two cases. Numerical modeling and theoretical analysis are combined with experiments on an electronic analog model of the system under study. The issues concerning physical realization of the dynamics of systems with a line of equilibria are considered. The question on whether oscillations in such systems can be classified as the self-sustained oscillations is raised.

Poincaré recurrence statistics as an indicator of chaos synchronization.

The dynamics of the autonomous and non-autonomous Rössler system is studied using the Poincaré recurrence time statistics. It is shown that the probability distribution density of Poincaré recurrences represents a set of equidistant peaks with the distance that is equal to the oscillation period and the envelope obeys an exponential distribution. The dimension of the spatially uniform Rössler attractor is estimated using Poincaré recurrence times. The mean Poincaré recurrence time in the non-autonomous Rössler system is locked by the external frequency, and this enables us to detect the effect of phase-frequency synchronization.

Stability and Noise-induced Transitions in an Ensemble of Nonlocally Coupled Chaotic Maps

The influence of noise on chimera states arising in ensembles of nonlocally coupled chaotic maps is studied. There are two types of chimera structures that can be obtained in such ensembles: phase and amplitude chimera states. In this work, a series of numerical experiments is carried out to uncover the impact of noise on both types of chimeras. The noise influence on a chimera state in the regime of periodic dynamics results in the transition to chaotic dynamics. At the same time, the transformation of incoherence clusters of the phase chimera to incoherence clusters of the amplitude chimera occurs. Moreover, it is established that the noise impact may result in the appearance of a cluster with incoherent behavior in the middle of a coherence cluster.

Local sensitivity of spatiotemporal structures

We present an index for the local sensitivity of spatiotemporal structures in coupled oscillatory systems based on the properties of local-in-space, finite-time Lyapunov exponents. For a system of nonlocally coupled Rössler oscillators, we show that variations of this index for different oscillators reflect the sensitivity to noise and the onset of spatial chaos for the patterns where coherence and incoherence regions coexist.

Coherence–Incoherence Transition and Properties of Different Types of Chimeras in a Network of Nonlocally Coupled Chaotic Maps

We explore the bifurcation transition from coherence to incoherence in an ensemble of nonlocally coupled logistic maps. It is shown that two types of chimera states, namely amplitude and phase, can be found in this network. We reveal a bifurcation mechanism by analyzing the evolution of space-time profiles and the coupling function with varying coupling coefficient and formulate the conditions for realizing the chimera states in the ensemble. The regularities are established for the evolution of cross-correlations of oscillations in the network elements at the bifurcations related to the coupling strength variation. We reveal the features of cross-correlations for phase and amplitude chimera states. It is also shown that the effect of time intermittency between the amplitude and phase chimeras can be realized in the considered ensemble.

Traveling waves and dynamical formation of autonomous pacemakers in a bistable medium with periodic boundary conditions

The problem of spatiotemporal pattern formation in the wall of arterial vesselsmay be reduced to 1D or 2D models of nonlinear active medium. We address this problem using the discrete array of non-oscillating (bistable) active units. We show how the specific choice of initial conditions in a 1D model with periodic boundary conditions triggers the self-sustained behaviour. We reveal the core of observed effects being the dynamical formation of localized (few-element size) autonomous pacemakers.