Related papers: From synchronization to multistability in two coup…
This paper has a double goal, the first one is to make a slight survey of some theoretical results about the existence of positively invariant curves that allow to describe important properties of the set of bounded orbits and its boundary…
We consider the stability of synchronized chaos in coupled map lattices and in coupled ordinary differential equations. Applying the theory of Hermitian and positive semidefinite matrices we prove two results that give simple bounds on…
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 study the completely synchronized states (CSSs) of a system of coupled logistic maps as a function of three parameters: interaction strength ($\varepsilon$), range of the interaction ($\alpha$), that can vary from first-neighbors to…
The mechanism of synchronization of oscillations in two identical coupled flow systems has beenstudied. The time (past the coupling onset) during which a synchronous oscillation regime is establisheddepends on the oscillation phase…
We consider a model where a population of diffusively coupled limit-cycle oscillators, described by the complex Ginzburg-Landau equation, interacts nonlocally via an inertial field. For sufficiently high intensity of nonlocal inertial…
Two oscillators coupled to a two-level system which in turn is coupled to an infinite number of oscillators (reservoir) are considered, bringing to light the occurrence of synchronization. A detailed analysis clarifies the physical…
In relation to spatiotemporal intermittency, as it can be observed in coupled map lattices, we study the stability of different wavelengths in competition. Introducing a two dimensional map, we compare its dynamics with the one of the whole…
We track the secondary bifurcations of coherent states in plane Couette flow and show that they undergo an incomplete periodic doubling cascade that ends with a crisis bifurcation. We introduce a symbolic dynamics for the orbits and show…
We investigate the convergence towards periodic orbits in discrete dynamical systems. We examine the probability that a randomly chosen point converges to a particular neighborhood of a periodic orbit in a fixed number of iterations, and we…
A method for the semiclassical quantization of chaotic maps is proposed, which is based on harmonic inversion. The power of the technique is demonstrated for the baker's map as a prototype example of a chaotic map.
We study the stability of the fixed-point solution of an array of mutually coupled logistic maps, focusing on the influence of the delay times, $\tau_{ij}$, of the interaction between the $i$th and $j$th maps. Two of us recently reported…
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…
A general technique for the periodic orbit quantization of systems with near-integrable to mixed regular-chaotic dynamics is introduced. A small set of periodic orbits is sufficient for the construction of the semiclassical recurrence…
Several coupled maps models are sketched and reviewed in this short communication. First, a discrete logistic type model that was proposed for the symbiotic interaction of two species. Second, a model of many of these symbiotic species…
In a previous paper we introduced examples of Hamiltonian mappings with phase space structures resembling circle packings. It was shown that a vast number of periodic orbits can be found using special properties. We now use this information…
A network of delay-coupled logistic maps exhibits two different synchronization regimes, depending on the distribution of the coupling delay times. When the delays are homogeneous throughout the network, the network synchronizes to a…
The critical behavior for intermittency is studied in two coupled one-dimensional (1D) maps. We find two fixed maps of an approximate renormalization operator in the space of coupled maps. Each fixed map has a common relavant eigenvaule…
Synchronisation between coupled oscillatory systems is a common phenomenon in many natural as well as technical systems. Varying the strength of coupling often leads to qualitative changes in the complex dynamics of the mutually coupled…
A coupled map model for the chaotic phase synchronization and its desynchronization phenomenon is proposed. The model is constructed by integrating the coupled kicked oscillator system, kicking strength depending on the complex state…