Related papers: Chaotifiying continuous-time systems by symmetry
We present a new solution for fundamental problems in nonlinear dynamical systems: finding, verifying, and stabilizing cycles. The solution we propose consists of a new control method based on mixing previous states of the system (or the…
Adaptive control technique is adopted to synchronize two identical non-autonomous systems with unknown parameters in finite time. A virtual unknown parameter is introduced in order to avoid the unknown parameters from appearing in the…
One or more small holes provide non-destructive windows to observe corresponding closed systems, for example by measuring long time escape rates of particles as a function of hole sizes and positions. To leading order the escape rate of…
We present a definition of chaotic Delone set, and establish the genericity of chaos in the space of $(\epsilon,\delta)$-Delone sets for $\epsilon\geq \delta$. We also present a hyperbolic analogue of the cut-and-project method that…
We introduce the notion of a quasistatic dynamical system, which generalizes that of an ordinary dynamical system. Quasistatic dynamical systems are inspired by the namesake processes in thermodynamics, which are idealized processes where…
We present a technique to control chaos in Hamiltonian systems which are close to integrable. By adding a small and simple control term to the perturbation, the system becomes more regular than the original one. We apply this technique to a…
Dynamical chaos is a term that encompasses a wide range of nonlinear phenomena such as turbulence, neuronal avalanches, weather patterns, and many others. However, despite much work in the field of chaos, its fundamental physical origin…
We consider the Kirchhoff equation on tori of any dimension and we construct solutions whose Sobolev norms oscillates in a chaotic way on certain long time scales. The chaoticity is encoded in the time between oscillations of the norm,…
Chaotic functions are characterized by sensitivity to initial conditions, transitivity, and regularity. Providing new functions with such properties is a real challenge. This work shows that one can associate with any Boolean network a…
A revised self-synchronizing stream cipher based on chaotic coupled maps is proposed. This system adds input and output functions aim to strengthen its security. The system performs basic floating-point analytical computation on real…
A new type of deterministic chaos for a system described by iterative two-dimensional maps is reported. The series being generated by the original map has an average upward trend while the first difference, which is the series of changes…
We consider the stability of synchronized chaos in coupled map lattices and in coupled ordinary differential equations. Applying the theory of Hermitian and positive semidefinite matrices we prove two results that give simple bounds on…
This note provides a general construction, and gives a concrete example of, forced ordinary differential equation systems that have these two properties: (a) for each constant input u, all solutions converge to a steady state but (b) for…
We consider a system of nonlocal equations driven by a perturbed periodic potential. We construct multibump solutions that connect one integer point to another one in a prescribed way. In particular, heteroclinc, homoclinic and chaotic…
The effect of impurities in a two-dimensional lattice of coupled nonlinear chaotic oscillators and their ability to control the dynamical behavior of the system are studied. We show that a single impurity can produce synchronized…
Proving the chaoticity of some dynamical systems is equivalent to solving the hardest problems in mathematics. Conversely, one argues that it is not unconceivable that classical physical systems may "compute the hard or even the…
Two replicas of spatially extended chaotic systems synchronize to a common spatio-temporal chaotic state when coupled above a critical strength. As a prototype of each single spatio-temporal chaotic system a lattice of maps interacting via…
A new approach is proposed to the analysis of generalized synchronization of multidimensional chaotic systems. The approach is based on the symbolic analysis of discrete sequences in the basis of a finite T-alphabet. In fact, the symbols of…
We study the regime of anticipated synchronization recently described on a number of dynamical systems including chaotic and noisy ones. We use simple linear caricatures to show the minimal setups able to reproduce the basic facts…
The supersymmetry method has proven to be a very powerful tool of study of the statistical properties of energy levels and eigenfunctions in disordered and chaotic systems. The aim of these lectures is to present a tutorial introduction to…