Related papers: Multistability, multiperiodicity, multichaos: in a…
Recent progress toward classifying low-dimensional chaos measured from time series data is described. This classification theory assigns a template to the time series once the time series is embedded in three dimensions. The template…
The phase ordering properties of lattices of band-chaotic maps coupled diffusively with some coupling strength $g$ are studied in order to determine the limit value $g_e$ beyond which multistability disappears and non-trivial collective…
We examine synchronization between identical chaotic systems. A rigorous criteria is presented which, if satisfied, guarantees that the coupling produces linearly stable synchronous motion. The criteria can also be used to design couplings…
A route to chaos is studied in 3-dimensional maps of logistic type. Mechanisms of period doubling for invariant closed curves (ICC) are found for specific 3-dimensional maps. These bifurcations cannot be observed for ICC in the…
A variety of nonlinear models of biological systems generate complex chaotic behaviors that contrast with biological homeostasis, the observation that many biological systems prove remarkably robust in the face of changing external or…
Introduced as a model for hyperchaos, the generalized R"ossler system of dimension N is obtained by linearly coupling N-3 additional degrees of freedom to the original R"ossler equation. Under variation of a single control parameter, it is…
This paper formulates a new approach to the study of chaos in discrete dynamical systems based on the notions of inverse ill-posed problems, set-valued mappings, generalized and multivalued inverses, graphical convergence of a net of…
Collective behavior is studied in globally coupled maps with distributed nonlinearity. It is shown that the heterogeneity enhances regularity in the collective dynamics. Low-dimensional quasiperiodic motion is often found for the…
Multimode fibres (MMFs) are attracting interest for complex spatiotemporal dynamics, and for ultrafast fibre sources, imaging and telecommunications. This new interest is based on three key properties: their high spatiotemporal complexity…
The collective behavior of a coupled map lattice having {\it unbounded} chaotic local dynamics is investigated through the properties of its mean field. The presence of unstable periodic orbits in the local maps determines the emergence of…
The relevance of chaos to evolution is discussed in the context of the origin and maintenance of diversity and complexity. Evolution to the edge of chaos is demonstrated in an imitation game. As an origin of diversity, dynamic clustering of…
This article is talking about the study constructive method of structural identification systems with chaotic dynamics. It is shown that the reconstructed attractors are a source of information not only about the dynamics but also on the…
We investigate a model of high-dimensional dynamical variables with all-to-all interactions that are random and non-reciprocal. We characterize its phase diagram and show that the model can exhibit chaotic dynamics. We show that the…
We consider a dissipative version of the standard nontwist map. Nontwist systems present a robust transport barrier, called the shearless curve, that becomes the shearless attractor when dissipation is introduced. This attractor can be…
A square lattice distribution of coupled oscillators that have heteroclinic cycle attractors is studied. In this system, we find a novel type of patterns that is spatially disordered and periodic in time. These patterns are limit cycle…
This paper is devoted to the study of nonautonomous multivalued semiflows and their associated pullback attractors. For this kind of dynamical systems we are able to characterize the upper and lower bounds of the attractor as complete…
Let f be a diffeomorphism of a compact finite dimensional boundaryless manifold M exhibiting infinitely many coexisting attractors. Assume that each attractor supports a stochastically stable probability measure and that the union of the…
A new computational technique based on the symbolic description utilizing kneading invariants is proposed and verified for explorations of dynamical and parametric chaos in a few exemplary systems with the Lorenz attractor. The technique…
We analyze stability of a system which contains an harmonic oscillator non-linearly coupled to its second harmonic, in the presence of a driving force. It is found that there always exists a critical amplitude of the driving force above…
We comment on mathematical results about the statistical behavior of Lorenz equations an its attractor, and more generally to the class of singular hyperbolic systems. The mathematical theory of such kind of systems turned out to be…