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We consider a family of singular maps as an example of a simple model of dynamical systems exhibiting the property of robust chaos on a well defined range of parameters. Critical boundaries separating the region of robust chaos from the…
Pattern formation and evolution in unsynchronizable complex networks are investigated. Due to the asymmetric topology, the synchronous patterns formed in complex networks are irregular and nonstationary. For coupling strength immediately…
Steady laminar flows through porous media spontaneously generate Lagrangian chaos at pore scale, with qualitative implications for a range of transport, reactive and biological processes. The characterization and understanding of mixing…
Synchronization transitions are investigated in coupled chaotic maps. Depending on the relative weight of linear versus nonlinear instability mechanisms associated to the single map two different scenarios for the transition may occur. When…
Lyapunov exponents of dynamical systems are defined from the rates of divergence of nearby trajectories. For stochastic systems, one typically assumes that these trajectories are generated under the "same noise realization". The purpose of…
This work describes the way that topological mixing and chaos in continua, as induced by discrete dynamical systems, can or can't be understood through topological conjugacy with symbolic dynamical systems. For example, there is no symbolic…
If you are given a simple three-dimensional autonomous quadratic system that has only one stable equilibrium, what would you predict its dynamics to be, stable or periodic? Will it be surprising if you are shown that such a system is…
We analyze probe data obtained from a toroidal magnetized plasma configuration suitable for studies of low-frequency gradient-driven instabilities. These instabilities give rise to field-aligned convection rolls analogous to Rayleigh-Benard…
In a generic dynamical system chaos and regular motion coexist side by side, in different parts of the phase space. The border between these, where trajectories are neither unstable nor stable but of marginal stability, manifests itself…
Upon addition of noise, chaotic motion in low-dimensional dynamical systems can sometimes be transformed into nonchaotic dynamics: namely, the largest Lyapunov exponent can be made nonpositive. We study this phenomenon in model systems with…
We study the topological dynamics by iterations of a piecewise continuous, non linear and locally contractive map in a real finite dimensional compact ball. We consider those maps satisfying the "separation property": different continuity…
We present new results of numerical simulations for driven vortex lattices in presence of random disorder at zero temperature. We show that the plastic dynamics of vortices display dissipative chaos. Intermittency "routes to chaos" have…
We consider a mechanism for area preserving Hamiltonian systems which leads to the enhanced probability, $P(\lambda, t)$, to find small values of the finite time Lyapunov exponent, $\lambda$. In our investigation of chaotic dynamical…
An important aspect of the recently introduced transient uncoupling scheme is that it induces synchronization for large values of coupling strength at which the coupled chaotic systems resist synchronization when continu- ously coupled.…
We treat $n$-dimensional piecewise-linear continuous maps with two pieces, each of which has exactly one unstable direction, and identify an explicit set of sufficient conditions for the existence of a chaotic attractor. The conditions…
A multi-dimensional switched system or multi-mode multi-dimensional ($M^3D$) system extends the classic switched system by allowing different subsystem dimensions. The stability problem of the $M^3D$ system, whose state transitions at…
It is shown that the asymptotic spectra of finite-time Lyapunov exponents of a variety of fully chaotic dynamical systems can be understood in terms of a statistical analysis. Using random matrix theory we derive numerical and in particular…
Strange nonchaotic attractors (SNA) arise in quasiperiodically driven systems in the neighborhood of a saddle node bifurcation whereby a strange attractor is replaced by a periodic (torus) attractor. This transition is accompanied by Type-I…
Characterizing the emergence of chaotic dynamics of complex networks is an essential task in nonlinear science with potential important applications in many fields such as neural control engineering, microgrid technologies, and ecological…
The stability analysis of a class of discontinuous discrete-time systems is studied in this paper. The system under study is modeled as a feedback interconnection of a linear system and a set-valued nonlinearity. An equivalent…