Jump intermittency as a second type of transition to and from generalized synchronization

Intermittency in predicting the behavior of stochastic systems using reservoir computing

A new behavior type of reservoir computing model for predicting dynamics of stochastic systems has been observed. It has been shown that when the control parameters of the predicted stochastic system and the reservoir computing model are turned, we observe intermittent behavior, i.e., close to the threshold parameter value the reservoir computing model demonstrates the accurate prediction most of the time, but there are time intervals during which the accurate prediction is interrupted by intervals characterized by the lack of prediction. The characteristics of the intermittency in predicting the behavior of the stochastic system correspond to the well-known on-off intermittency. The concept of the effective noise to describe the quality of prediction is proposed, and the technique of its amplitude value estimation is developed.

Intermittent generalized synchronization and modified system approach: Discrete maps

The present work deals with the intermittent generalized synchronization regime observed near the boundary of generalized synchronization. The intermittent behavior is considered in the context of two observable phenomena, namely, (i) the birth of the asynchronous stages of motion from the complete synchronous state and (ii) the multistability in detection of the synchronous and asynchronous states. The mechanisms governing these phenomena are revealed and described in this paper with the help of the modified system approach for unidirectionally coupled model oscillators with discrete time.

Collective dynamics of coupled Lorenz oscillators near the Hopf boundary: Intermittency and chimera states

We study collective dynamics of networks of mutually coupled identical Lorenz oscillators near a subcritical Hopf bifurcation. Such systems exhibit induced multistable behavior with interesting spatiotemporal dynamics including synchronization, desynchronization, and chimera states. For analysis, we first consider a ring topology with nearest-neighbor coupling and find that the system may exhibit intermittent behavior due to the complex basin structures and dynamical frustration, where temporal dynamics of the oscillators in the ensemble switches between different attractors. Consequently, different oscillators may show a dynamics that is intermittently synchronized (or desynchronized), giving rise to intermittent chimera states. The behavior of the intermittent laminar phases is characterized by the characteristic time spent in the synchronization manifold, which decays as a power law. Such intermittent dynamics is quite general and is also observed in an ensemble of a large number of oscillators arranged in variety of network topologies including nonlocal, scale-free, random, and small-world networks.

Synchronization of a Network Composed of Stochastic Hindmarsh–Rose Neurons

An algorithm for synchronization of a network composed of interconnected Hindmarsh–Rose neurons is presented. Delays are present in the interconnections of the neurons. Noise is added to the controlled input of the neurons. The synchronization algorithm is designed using convex optimization and is formulated by means of linear matrix inequalities via the stochastic version of the Razumikhin functional. The recovery and the adaptation variables are also synchronized; this is demonstrated with the help of the minimum-phase property of the Hindmarsh–Rose neuron. The results are illustrated by an example.

On multistability near the boundary of generalized synchronization in unidirectionally coupled chaotic systems

Multistability in the intermittent generalized synchronization regime in unidirectionally coupled chaotic systems has been found. To study such a phenomenon, the method for revealing the existence of multistable states in interacting systems being the modification of an auxiliary system approach has been proposed. The efficiency of the method has been testified using the examples of unidirectionally coupled logistic maps and Rössler systems being in the intermittent generalized synchronization regime. The quantitative characteristic of multistability has been introduced into consideration.