Systems of strongly coupled chaotic maps generically exhibit collective behavior emerging out of extensive chaos. We show how the well-known renormalization group (RG) of unimodal maps can be extended to the coupled systems, and in particular to coupled map lattices (CMLs) with local diffusive coupling. The RG relation derived for CMLs is nonperturbative, i.e., not restricted to a particular cl...

We investigate the complexity of short symbolic sequences of chaotic dynamical systems by using lossless compression algorithms. In particular, we study Non-Sequential Recursive Pair Substitution (NSRPS), a lossless compression algorithm first proposed by W. Ebeling et al. [Math. Biosc. 52, 1980] and Jiménez-Montaño et al. [arXiv:cond-mat/0204134, 2002]) which was subsequently shown to be optim...

We describe the transfer operator approach to coupled map lattices (CML) in cases where the local map is expanding but has no Markov partition (e.g. a general tent map). The coupling is allowed to be non-local, but the total innuence of all sites j 6 = i on site i must be small. The main technical tool are lattice-size independent estimates of Lasota-Yorke type which show that the transfer (Per...

‎in this text we prove that in generalized shift dynamical system $(x^gamma,sigma_varphi)$‎ ‎for finite discrete $x$ with at least two elements‎, ‎infinite countable set $gamma$ and‎ ‎arbitrary map $varphi:gammatogamma$‎, ‎the following statements are equivalent‎: ‎ - the dynamical system $(x^gamma,sigma_varphi)$ is‎ li-yorke chaotic;‎ - the dynamical system $(x^gamma,sigma_varphi)$ has‎ an scr...

Using a new key management system and Jacobian elliptic map, speech encryption scheme has been developed for secure communication data. map-based as novel method to improve the existing methods' drawbacks, such poor quality in decrypted signals, residual intelligibility, high computational complexity, low-key space. map solution, cryptosystem was created. The proposed scheme's performance is ev...

a watermarking scheme for Grayscale image isproposed based on a family of the chaotic maps and discretecosine transform. Jacobian Elliptic mapis employed to encrypt ofwatermarked logo. Piecewise nonlinear chaotic map is also usedto determine the location of DCT coefficients for the watermarkembedding. The purpose of this algorithm is to improve theshortcoming of watermarking such as small key s...