For an irreducible transition matrix A of size m × m, which is not a permutation, a map f : X → X is said to be strictly A-coupled-expanding if there are nonempty sets V1, . . . , Vm ⊂ X such that the distance between any two of them is positive and f(Vi) ⊃ Vj holds whenever aij = 1. This paper presents two theorems that give sufficient conditions for a strictly A-coupledexpanding map to be cha...

We analyze a system of globally coupled logistic maps with asynchronous updating. We show that its dynamics differs considerably from that of the synchronous case. For growing values of the coupling intensity, an inverse bifurcation cascade replaces the structure of clusters and ordering in the phase diagram. We present numerical simulations and an analytical description based on an effective s...

We study the invariant measure or the stationary density of a coupled discrete dynamical system as a function of the coupling parameter ǫ (0 < ǫ < 1/4). The dynamical system considered is chaotic and unsynchronized for this range of parameter values. We find that the stationary density, restricted on the synchronization manifold, is a fractal function. We find the lower bound on the fractal dim...

The dynamics of a globally coupled, logistic map lattice is explored over a parameter plane consisting of the coupling strength, varepsilon, and the map parameter, a. By considering simple periodic orbits of relatively small lattices, and then an extensive set of initial-value calculations, the phenomenology of solutions over the parameter plane is broadly classified. The lattice possesses many...

When identical chaotic oscillators interact, a state of complete or partial synchronization may be attained in which the motion is restricted to an invariant manifold of lower dimension than the full phase space. Riddling of the basin of attraction arises when particular orbits embedded in the synchronized chaotic state become transversely unstable while the state remains attracting on the aver...

Internal mapping of the external environment is carried out using the receptive fields of topographic neurons in the brain, and in a normal barn owl the aural and visual subcortical maps are aligned from early experiences. However, instantaneous misalignment of the aural and visual stimuli has been observed to result in adaptive behavior, manifested by functional and anatomical changes of the a...

The dynamics of coupled intermittent maps is used to model the correlated structure of genomic sequences. The use of intermittent maps, as opposed to other simple chaotic maps, is particularly suited for the production of long range correlation features which are observed in the genomic sequences of higher eucaryotes. A weighted network approach to symbolic sequences is introduced and it is sho...

In our previous study, we observed the interesting phenomena on asymmetrical chaotic coupled systems. It is that the ratio of synchronization time of the one subsystem group increases in spite of increasing parameter mismatches in the other subsystem. In this study, an asymmetrical globally coupled maps is proposed and investigated, in order to explain the these phenomena. Asymmetry of the syst...

The dynamics of coupled intermittent maps is used to model the correlated structure of genomic sequences. The use of intermittent maps, as opposed to other simple chaotic maps, is particularly suited for the production of long-range correlation features which are observed in the genomic sequences of higher eucaryotes. A weighted network approach to symbolic sequences is introduced, and it is sh...

Using a renormalization method, we study the critical behavior for intermittency in two coupled one-dimensional (1D) maps. We find two fixed maps of the renormalization transformation. They all have common relevant eigenvalues associated with scaling of the control parameter of the uncoupled 1D map. However, the relevant “coupling eigenvalues” associated with coupling perturbations vary dependi...