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

Abstract

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.

Double-well chimeras in 2D lattice of chaotic bistable elements

“…It means that all the lattice elements are located either in positive or negative well. These chimera states which we find here for the lattice are similar to the phase and amplitude chimeras previously detected for the rings of logistic maps and chaotic self-sustained oscillators [43,44,45]. The illustrative example of the structure involving phase and amplitude chimeras is shown in fig.…”

“…The main dynamical regimes observed for the lattice Eq. (1) are full chaotic synchronization, partial coherence (oscillating synchronization) according to the terminology used in [45], chimera states and spatial incoherence (in fig. 3 A, B, C and D, respectively).…”

“…Elements from the coherent cluster act in synchrony, while the oscillators from the incoherent cluster are not correlated and form a domain of spatial chaos with fixed borders. Chimeras were found in ensembles of phase oscillators [27,28,29,30,31,32], periodic self-sustained oscillators [33,34,35,36,37,38,39], chaotic oscillators and chaotic return maps [40,41,42,43,44,45,46], networks of oscillatory elements containing blocks of excitable elements [47] or only excitable units [48]. Chimera structures were obtained not only in numerical simulations but also in experiments [49,50,51,52,53,54].…”

“…Apparently, hyperbolic chaos impedes the occurrence of chimeras [42]. The models of chaotic systems (such as logistic map, Rössler oscillator) demonstrating chimera states in networks of interacting units [40,41,42,43,44,45] are characterized by the regime of nonhyperbolic chaos, which occurs due to a cascade of period doubling bifurcations (Feigenbaum scenario [62]). The dynamics of ensembles of such elements with local interactions (for example, [12,16,17,63,64]) shows a high level of multistability with a variety of coexisting states in the case of weak coupling.…”

Solitary states in a 2D lattice of bistable elements with global and close to global interaction

“…В области промежуточных значений связи характер динамики элементов ансамбля во времени меняется, а в пространстве мо-гут возникать различные структуры, связанные с эффектами кластерной синхронизации и пространственной перемежаемости (см., например, [5,13,14,18,26,32]). В ансамблях хао-тических осцилляторов с нелокальным взаимодействием переход «когерентный хаос -неко-герентный хаос» сопровождается возникновением химерных структур [4,6,27,29,36,41].…”