Susceptibility of transient chimera states

Abstract

Chaotic dynamics of a dynamical system is not necessarily persistent. If there is (without any active intervention from outside) a transition towards a (possibly nonchaotic) attractor, this phenomenon is called transient chaos, which can be observed in a variety of systems, e.g., in chemical reactions, population dynamics, neuronal activity, or cardiac dynamics. Also, chimera states, which show coherent and incoherent dynamics in spatially distinct regions of the system, are often chaotic transients. In many practical cases, the control of the chaotic dynamics (either the termination or the preservation of the chaotic dynamics) is desired. Although the self-termination typically occurs quite abruptly and can so far in general not be properly predicted, previous studies showed that in many systems a 'terminal transient phase" (TTP) prior to the self-termination existed, where the system was less susceptible against small but finite perturbations in different directions in state space. In this study, we show that, in the specific case of chimera states, these susceptible directions can be related to the structure of the chimera, which we divide into the coherent part, the incoherent part and the boundary in between. That means, in practice, if self-termination is close we can identify the direction of perturbation which is likely to maintain the chaotic dynamics (the chimera state). This finding improves the general understanding of the state space structure during the TTP, and could contribute also to practical applications like future control strategies of epileptic seizures which have been recently related to the collapse of chimera states.

Chimera states in multiplex networks: Chameleon-like across-layer synchronization

“…Future work should study in more detail the role of the phase lag parameter in individual layers with regard to the emergence of chimera states in multilayer networks. Furthermore, the transient nature of chimera states 44,45,59,60 should be further analyzed. A question which should be addressed is how the inter-layer coupling influences the system's overall stability and lifetime distributions (see also Refs.…”

Spiral wave chimera-like transient dynamics in three-dimensional grid of diffusive ecological systems

“…Here we estimate the transient time for the transition from initial dynamics to the long term dynamics taking account of the effect of diffusion coefficients. Previously, transient chimera states [71][72][73] were reported by several researchers in mostly 1D and 2D domains for smaller system sizes. However, these studies mention a sudden collapse of transient chimera states and abrupt transition to coherent states as the time grows.…”

Focusing on transient chaos

“…In both cases, the parameters of the system are identified, for which the system shows rotating spiral-like patterns with randomized core regions-so called spiral wave chimera states. It is expected that these chimera states behave as chaotic transients in networks of small size [4,5] (although this property is not explored in [3]).…”