A Proof for the Existence of Chaos in Diffusively Coupled Map Lattices with Open Boundary Conditions
نویسندگان
چکیده
We first study how to make use of the Marotto theory to prove rigorously the existence of the Li-Yorke chaos in diffusively coupled map lattices with open boundary conditions i.e., a highdimensional discrete dynamical system . Then, the recent 0-1 test for chaos is applied to confirm our theoretical claim. In addition, we control the chaotic motions to a fixed point with delay feedback method. Numerical results support the theoretical analysis.
منابع مشابه
Kato's chaos and P-chaos of a coupled lattice system given by Garcia Guirao and Lampart which is related with Belusov-Zhabotinskii reaction
In this article, we further consider the above system. In particular, we give a sufficient condition under which the above system is Kato chaotic for $eta=0$ and a necessary condition for the above system to be Kato chaotic for $eta=0$. Moreover, it is deduced that for $eta=0$, if $Theta$ is P-chaotic then so is this system, where a continuous map $Theta$ from a compact metric space $Z$ to itse...
متن کاملDynamics of inhomogeneous one – dimensional coupled map lattices
We study the dynamics of one–dimensional discrete models of one–component active medium built up of spatially inhomogeneous chains of diffusively coupled piecewise linear maps. The nonhomogeneities (" defects ") are treated in terms of parameter difference in the corresponding maps. Two types of space defects are considered: periodic and localized. We elaborate analytic approach to obtain the r...
متن کاملThe existence results for a coupled system of nonlinear fractional differential equations with multi-point boundary conditions
In this paper, we study a coupled system of nonlinear fractional differential equations with multi-point boundary condi- tions. The differential operator is taken in the Riemann-Liouville sense. Applying the Schauder fixed-point theorem and the contrac- tion mapping principle, two existence results are obtained for the following system D^{alpha}_{0+}x(t)=fleft(t,y(t),D^{p}_{0+}y(t)right), t in (0,...
متن کاملSynchronization in Coupled Map Lattices with Periodic Boundary Condition
We consider a lattice of coupled logistic maps with periodic boundary condition. We prove that synchronization and almost synchronization occur for the case of 1D lattice with lattice size n = 2, 3, 4 provided the coupling strength c is chosen in a suitable open interval contained in [0, 12 ]. For the case of lattice size n ≥ 4, we also show the numerical results of (almost) synchronized chaoti...
متن کاملThe Distribution of periodic and Aperiodic Pattern Evolutions in Rings of Diffusively Coupled Maps
This work reports a systematic investigation of the distribution of periodic and aperiodic patternevolution in rings of diffusively coupled quadratic maps. Our main motivation here is the wish to investigate whether lattices of coupled maps can be effectively used to simulate a plethora of phenomena associated with climatic variability and change. Presently, simulations of these phenomena reduc...
متن کامل