Related papers: Folded Bifurcation in Coupled Asymmetric Logistic …

We introduce new models of very weakly coupled logistic and tent maps for which orbits of very long period are found. The length of these periods is far greater than one billion. The property of these models relatively to the distribution…

Fundamental problems of periodicity and transient process to periodicity of chaotic trajectories in computer realization with finite computation precision is investigated by taking single and coupled Logistic maps as examples. Empirical…

We provide an analytical proof of the existence of a stable periodic orbit contained in the region of coexistence of the three species of a tritrophic chain. The method used consists in analyzing a triple Hopf bifurcation. For some values…

Recent investigations on the bifurcations in switching circuits have shown that many atypical bifurcations can occur in piecewise smooth maps which can not be classified among the generic cases like saddle-node, pitchfork or Hopf…

The idea that chaos could be a useful tool for analyze nonlinear systems considered in this paper and for the first time the two time scale property of singularly perturbed systems is analyzed on chaotic attractor. The general idea…

Differentiable conjugacies link dynamical systems that share properties such as the stability multipliers of corresponding orbits. It provides a stronger classification than topological conjugacy, which only requires qualitative similarity.…

A one-dimensional chain of sporadic maps with asymmetric nearest neighbour couplings is numerically studied. It is shown that in the region of strong asymmetry the system becomes spatially fully synchronized, even in the thermodinamic…

Time-delay chaotic systems refer to the hyperchaotic systems with multiple positive Lyapunov exponents. It is characterized by more complex dynamics and a wider range of applications as compared to those non-time-delay chaotic systems. In a…

This study examines the dynamical properties of the Ikeda map, with a focus on bifurcations and chaotic behavior. We investigate how variations in dissipation parameters influence the system, uncovering shrimp-shaped structures that…

We investigate the processes of synchronization and phase ordering in a system of globally coupled maps possessing bistable, chaotic local dynamics. The stability boundaries of the synchronized states are determined on the space of…

This paper deals with various routes to hyperchaos with all three positive Lyapunov exponents in a three-dimensional quadratic map. The map under consideration displays strong hyperchaoticity in the sense that in a wider range of parameter…

We prove that spiral sinks (stable foci of vector fields) can be transformed into strange attractors exhibiting sustained, observable chaos if subjected to periodic pulsatile forcing. We show that this phenomenon occurs in the context of…

In this work we consider a general class of $2$-dimensional hybrid systems. Assuming that the system possesses an attracting equilibrium point, we show that, when periodically driven with a square-wave pulse, the system possesses a periodic…

We perform spectral simulations of dynamo for magnetic Prandtl number of one with Taylor-Green forcing. We observe dynamo transition through a supercritical pitchfork bifurcation. Beyond the transition, the numerical simulations reveal…

It is shown how different globally coupled map systems can be analyzed under a common framework by focusing on the dynamics of their respective global coupling functions. We investigate how the functional form of the coupling determines the…

We analyze the asymptotic states in the partially ordered phase of a system of globally coupled logistic maps. We confirm that, regardless of initial conditions, these states consist of a few clusters, and they properly belong in the…

In this work we study numerically a lattice composed of two parameter single quartic maps with local diffusive coupling. We find large regions over the parameter space where the single quartic map is periodic and the coupled system is not…

In this work we investigate the spatiotemporal behaviour of lattices of coupled chaotic logistic maps, where the coupling between sites has a nonlinear form. We show that the stable range of the spatiotemporal fixed point state is…

Coupled map lattices have been widely used as models in several fields of physics, such as chaotic strings, turbulence, and phase transitions, as well as in other disciplines, such as biology (ecology, evolution) and information processing.…

Dynamical behaviour of discrete dynamical systems has been investigated extensively in the past few decades. However, in several applications, long term memory plays an important role in the evolution of dynamical variables. The definition…