Related papers: Strange nonchaotic attractors in noise driven syst…
Chaotic bursting behaviors have been observed by many authors in neural dynamics mainly in the transition between different kinds of bursting behavior. As a well-known three-dimensional ODEs model with various bursting solutions, the…
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…
We study numerically chaotic behavior associated with a hyperbolic strange attractor of Plykin type in the model of Hunt, an artificially constructed dynamical system with continuous time. There are presented portraits of the attractor,…
A theory on bi-spatial random attractors developed recently by Li \emph{et al.} is extended to study stochastic Fitzhugh-Nagumo system driven by a non-autonomous term as well as a general multiplicative noise. By using the so-called notions…
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…
Investigating the possibility of applying techniques from linear systems theory to the setting of nonlinear systems has been the focus of many papers. The pseudo linear form representation of nonlinear dynamical systems has led to the…
Chaotic itinerancy is a frequently observed phenomenon in high-dimensional and nonlinear dynamical systems, and it is characterized by the random transitions among multiple quasi-attractors. Several studies have revealed that chaotic…
We study local and global stability of nonhyperbolic chaotic attractors contaminated by noise. The former is given by the maximum distance of a noisy trajectory from the noisefree attractor, while the latter is provided by the minimal…
The phenomenon of Stochastic Resonance (SR) is observed in a completely deterministic setting - with thermal noise being replaced by one-dimensional chaos. The piecewise linear map investigated in the paper shows a transition from…
The spontaneous transitions between D-dimensional spatial maps in an attractor neural network are studied. Two scenarios for the transition from on map to another are found, depending on the level of noise: (1) through a mixed state, partly…
This paper deals with various routes to hyperchaos with all three positive Lyapunov exponents in a three-dimensional quadratic map. The map under consideration displays strong hyperchaoticity in the sense that in a wider range of parameter…
The realization of novel scenario involving transitions between different types of chaotic attractors is investigated for the Rossler system. Characteristic features indicative of the presence of generalized intermittency scenario in this…
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…
We consider transitions to chaos in random dynamical systems induced by an increase of noise amplitude. We show how the emergence of chaos (indicated by a positive Lyapunov exponent) in a logistic map with bounded additive noise can be…
We study the effect that the injection of a common source of noise has on the trajectories of chaotic systems, addressing some contradictory results present in the literature. We present particular examples of 1-d maps and the Lorenz…
We present a neurobiologically--inspired stochastic cellular automaton whose state jumps with time between the attractors corresponding to a series of stored patterns. The jumping varies from regular to chaotic as the model parameters are…
In nonlinear systems analysis, minor fractions of higher-order dynamics are often neglected for simplicity. Here, we show that machine epsilon levels of parasitic higher-order dynamics due to computer roundoff alone can cause divergence of…
The global asymptotic behavior of a stochastic Hopfield neural network model (HNNM) with delays is explored by studying the existence and structure of random attractors. It is first proved that the trajectory field of the stochastic delayed…
We show that the classic example of quasiperiodically forced maps with strange nonchaotic attractors described by Grebogi et al and Herman in the mid-1980s have some chaotic properties. More precisely, we show that these systems exhibit…
In this paper, we demonstrate, first in literature known to us, that potential functions can be constructed in continuous dissipative chaotic systems and can be used to reveal their dynamical properties. To attain this aim, a Lorenz-like…