Synchronized Attractors and Phase Entrained with Cavity Loss of the Coupled Laser’s Map

The laser differential equations are used to transform them into identical coupled maps. Valuable results are deduced during analytical and numerical studies on cavity loss. Phase and spatiotemporal synchronized attractors are observed via quasi-chaos under a certain range of controlling parameters, and symmetry breaking of chaotic attractors due to collision with their basin boundaries, and transpire differently from the previous attractors. During the numerical simulation, it is found that the sequence of repeated strange attractors if the coupling strength further increases, which are orthogonal mirror images (the dynamics of the system is the same at different values of controlling parameters). Moreover, it can help us to predict future problems and their solutions based on current issues, if we develop this model in more general.

Bifurcations in 2D Spatiotemporal Maps

In this work, we give theoretical and numerical analyses for local bifurcations of 2D spatiotemporal discrete systems of the form [Formula: see text] where [Formula: see text] is a real nonlinear function, [Formula: see text] and [Formula: see text] are two independent integer variables, representing respectively a spatial coordinate and the time. On the basis of the spectral theory, we derive the conditions under which the local bifurcations such as flip and fold occur at the fixed points for some parameter values. As a case-study, a quite complex system, [Formula: see text]D spatiotemporal dynamic given by two coupled logistic maps, named [Formula: see text]D logistic coupled maps ([Formula: see text]D-LCM) is considered. The proposed map provides a reliable experimental and theoretical basis for identifying some cases of local bifurcations.

Chimeras and Clusters Emerging from Robust-Chaos Dynamics

We show that dynamical clustering, where a system segregates into distinguishable subsets of synchronized elements, and chimera states, where differentiated subsets of synchronized and desynchronized elements coexist, can emerge in networks of globally coupled robust-chaos oscillators. We describe the collective behavior of a model of globally coupled robust-chaos maps in terms of statistical quantities and characterize clusters, chimera states, synchronization, and incoherence on the space of parameters of the system. We employ the analogy between the local dynamics of a system of globally coupled maps with the response dynamics of a single driven map. We interpret the occurrence of clusters and chimeras in a globally coupled system of robust-chaos maps in terms of windows of periodicity and multistability induced by a drive on the local robust-chaos map. Our results show that robust-chaos dynamics does not limit the formation of cluster and chimera states in networks of coupled systems, as it had been previously conjectured.

Coupled Fixed Point Theorems Employing CLR-Property on V -Fuzzy Metric Spaces

The introduction of the common limit range property on V -fuzzy metric spaces is the foremost aim of this paper. Furthermore, significant results for coupled maps are proven by employing this property on V -fuzzy metric spaces. More precisely, we introduce the notion of C L R Ω -property for the mappings Θ : M × M → M and Ω : M → M . We utilize our new notion to present and prove our new fixed point results.