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This article studies the rotational dynamics of three identical coupled pendulums. There exist two parameter areas where the in-phase rotational motion is unstable and out-of-phase rotations are realized. Asymptotic theory is developed that…

Strange nonchaotic attractors (SNAs) in noise driven systems are investigated. Before the transition to chaos, due to the effect of noise, a typical trajectory will wander between the periodic attractor and its nearby chaotic saddle in an…

In this paper, we present a unified framework of multiple attractors including multistability, multiperiodicity and multichaos. Multichaos, which means that the chaotic solution of a system lies in different disjoint invariant sets with…

We explore the behaviour of an ensemble of chaotic oscillators coupled only to an external chaotic system, whose intrinsic dynamics may be similar or dissimilar to the group. Counter-intuitively, we find that a dissimilar external system…

We present a control scheme that is able to find and stabilize an unstable chaotic regime in a system with a large number of interacting particles. This allows us to track a high dimensional chaotic attractor through a bifurcation where it…

We numerically and analytically analyze transitions between different synchronous states in a network of globally coupled phase oscillators with attractive and repulsive interactions. The elements within the attractive or repulsive group…

Following the long-lived qualitative-dynamics tradition of explaining behavior in complex systems via the architecture of their attractors and basins, we investigate the patterns of switching between qualitatively distinct trajectories in a…

Continuous and discrete time systems possessing strange non-chaotic attractors are under investigation. It is demonstrated that unpredictable trajectories exist in the dynamics. A recent numerical technique, the sequential test, is utilized…

We study the effect of common noise on coupled active rotators. While such a noise always facilitates synchrony, coupling may be attractive or repulsing. We develop an analytical approach based on a transformation to approximate…

Despite their apparent simplicity, random Boolean networks display a rich variety of dynamical behaviors. Much work has been focused on the properties and abundance of attractors. We here derive an expression for the number of attractors in…

We investigate an oscillator linearly coupled with a one-dimensional Ising system. The coupling gives rise to drastic changes both in the oscillator statics and dynamics. Firstly, there appears a second order phase transition, with the…

We observe chaotic dynamics in a damped linear oscillator, which is driven only at certain regions of phase space. Both deterministic and random drives are studied. The dynamics is characterized using standard techniques of nonlinear…

We consider an autonomous system constructed as modification of the logistic differential equation with delay that generates successive trains of oscillations with phases evolving according to chaotic maps. The system contains two feedback…

Certain nonlinear systems can switch between dynamical attractors occupying different regions of phase space, under variation of parameters or initial states. In this work we exploit this feature to obtain reliable logic operations. With…

Synchronization is a widespread phenomenon observed in physical, biological, and social networks, which persists even under the influence of strong noise. Previous research on oscillators subject to common noise has shown that noise can…

We investigate phase synchronization between two identical or detuned response oscillators coupled to a slightly different drive oscillator. Our result is that phase synchronization can occur between response oscillators when they are…

A new approach to analysis of the synchronization of chaotic oscillations in two (or more) coupled oscillators is described that makes it possible to reveal changes in the structure of attractors and detect the appearance of intermittency.…

We study sustained oscillations in two-dimensional oscillator systems driven by Rayleigh-type negative friction. In particular we investigate the influence of mismatch of the two frequencies. Further we study the influence of external noise…

Two novel phenomena for unidirectionally coupled 3-cell Hopfield neural networks (HNNs) are investigated. The first one is the persistence of chaos, which means the permanency of sensitivity and infinitely many unstable periodic…

Multi--stability in the response of a ferrimagnetic spin resonator to an externally applied driving is experimentally studied. The observed multi--stability cannot be derived from any master equation that linearly depends on the spins'…