Networks Of Chaotic Maps Research Articles

Chimera resonance in networks of chaotic maps.

We explore numerically the impact of additive Gaussian noise on the spatiotemporal dynamics of ring networks of nonlocally coupled chaotic maps. The local dynamics of network nodes is described by the logistic map, the Ricker map, and the Henon map. 2D distributions of the probability of observing chimera states are constructed in terms of the coupling strength and the noise intensity and for several choices of the local dynamics parameters. It is shown that the coupling strength range can be the widest at a certain optimum noise level at which chimera states are observed with a high probability for a large number of different realizations of randomly distributed initial conditions and noise sources. This phenomenon demonstrates a constructive role of noise in analogy with the effects of stochastic and coherence resonance and may be referred to as chimera resonance.

Controlling chimera and solitary states by additive noise in networks of chaotic maps

We study numerically the spatio-temporal dynamics of ring networks of coupled discrete-time systems in the presence of additive noise. The robustness of chimera states with respect to noise perturbations is explored for two ensembles in which the individual elements are described by either logistic maps or Henon maps in the chaotic regime. The influence of noise on the behavior of solitary states is investigated for a ring of nonlocally coupled Lozi maps. Numerical simulations are performed for a set of different noise realizations and random initial conditions to provide reliable statistical data. The type of dynamics of the considered networks is quantified by using a cross-correlation coefficient. We find that there is a finite and sufficiently wide region with respect to the coupling strength and the noise intensity where the probability of observing the chimeras and solitary states is high.

Stability of synchronous state in networks of chaotic maps by matrix measure approach

Stability of synchronous state in networks of chaotic maps by matrix measure approach

One-way hash function construction based on chaotic map network

A novel chaotic hash algorithm based on a network structure formed by 16 chaotic maps is proposed. The original message is first padded with zeros to make the length a multiple of four. Then it is divided into a number of blocks each contains 4 bytes. In the hashing process, the blocks are mixed together by the chaotic map network since the initial value and the control parameter of each tent map are dynamically determined by the output of its neighbors. To enhance the confusion and diffusion effect, the cipher block chaining (CBC) mode is adopted in the algorithm. Theoretic analyses and numerical simulations both show that the proposed hash algorithm possesses good statistical properties, strong collision resistance and high flexibility, as required by practical keyed hash functions.

MULTISTABILITY, PHASE DIAGRAMS AND STATISTICAL PROPERTIES OF THE KICKED ROTOR: A MAP WITH MANY COEXISTING ATTRACTORS

We investigate the prevalence of multistability in the parameter space of the kicked rotor map. We report high-resolution phase diagrams showing how the density of attractors and the density of periods vary as a function of both model parameters. Our diagrams illustrate density variations that exist when moving between the familiar conservative and strongly dissipative limits of the map. We find the kicked rotor to contain multistability regions with more than 400 coexisting attractors. This fact makes the rotor a promising high-complexity local unit to investigate synchronization in networks of chaotic maps, in both regular and complex topologies.

Random global coupling induces synchronization and nontrivial collective behavior in networks of chaotic maps

The phenomena of synchronization and nontrivial collective behavior are studied in a model of coupled chaotic maps with random global coupling. The mean field of the system is coupled to a fraction of elements randomly chosen at any given time. It is shown that the reinjection of the mean field to a fraction of randomly selected elements can induce synchronization and nontrivial collective behavior in the system. The regions where these collective states emerge on the space of parameters of the system are calculated.

Impact of bistability in the synchronization of chaotic maps with delayed coupling and complex topologies

We investigate the impact of bistability in the emergence of synchronization in networks of chaotic maps with delayed coupling. The existence of a single finite attractor of the uncoupled map is found to be responsible for the emergence of synchronization. No synchronization is observed when the local dynamics has two competing chaotic attractors whose orbits are dense on the same interval. This result is robust for regular networks with variable ranges of interaction and for more complex topologies.

Consequences of nonlocal connections in networks of chaotic maps under threshold activated coupling.

We study the effects of random nonlocal connections on networks of chaotic maps under threshold activated coupling. In threshold regimes where a large number of unsynchronized attractors occur under regular connections, we show how nonlocal rewirings yield synchronized networks. However, the dependence of the synchronized fraction on the fraction of randomized nonlocal links is typically nonmonotonic here. Further, the mean time to reach synchronization with respect to the fraction of rewiring also indicates an optimum degree of nonlocality for which synchronization is most efficiently achieved.