Related papers: Synchronization of Random Linear Maps
A shift-periodic map is a one-dimensional map from the real line to itself which is periodic up to a linear translation and allowed to have singularities. It is shown that iterative sequences $x_{n+1}=F(x_n)$ generated by such maps display…
We investigate the synchronization dynamics in a chain of coupled chaotic maps organized in a single-parent family tree, whose properties can be captured considering each parent node connected to two children, one of which also serves as…
The scaling behaviour of the Lyapunov exponent near the transition to chaos via type-III intermittency is determined for a generic map. A critical exponent $\beta$ expressing the scaling of the Lyapunov exponent as a function of both, the…
This paper presents new sufficient conditions for convergence and asymptotic or exponential stability of a stochastic discrete-time system, under which the constructed Lyapunov function always decreases in expectation along the system's…
Instabilities in 1D spatially extended systems are studied with the aid of both temporal and spatial Lyapunov exponents. A suitable representation of the spectra allows a compact description of all the possible disturbances in tangent…
A condition for the synchronizability of a pair of PDE systems, coupled through a finite set of variables, is commonly the existence of internal synchronization or internal coherence in each system separately. The condition was previously…
A strong analogy is found between the evolution of localized disturbances in extended chaotic systems and the propagation of fronts separating different phases. A condition for the evolution to be controlled by nonlinear mechanisms is…
In this paper, we study Markovian random iterations of maps on standard measurable spaces. We establish a one-to-one correspondence between stationary measures and a certain class of invariant measures of a Markovian random iteration,…
We study the local complete synchronization of discrete-time dynamical networks with time-varying couplings. Our conditions for the temporal variation of the couplings are rather general and include both variations in the network structure…
Deterministic equilibrium flows in transport networks can be investigated by means of Markov's processes defined on the dual graph representations of the network. Sustained movement patterns are generated by a subset of automorphisms of the…
We point out the existence of a transition from partial to global generalized synchronization (GS) in symmetrically coupled structurally different time-delay systems of different orders using the auxiliary system approach and the mutual…
We study coupled dynamics on networks using symbolic dynamics. The symbolic dynamics is defined by dividing the state space into a small number of regions (typically 2), and considering the relative frequencies of the transitions between…
The Lyapunov exponent characterizes an exponential growth rate of the difference of nearby orbits. A positive Lyapunov exponent is a manifestation of chaos. Here, we propose the Lyapunov pair, which is based on the generalized Lyapunov…
A basic result in synchronization of linear systems via output coupling is presented. For identical discrete-time linear systems that are detectable from their outputs and neutrally stable, it is shown that a linear output feedback law…
Lyapunov exponents are well-known characteristic numbers that describe growth rates of perturbations applied to a trajectory of a dynamical system in different state space directions. Covariant (or characteristic) Lyapunov vectors indicate…
In this paper, synchronization of identical switched chaotic systems is explored based on Lyapunov theory of guaranteed stability. Concepts from robust control principles and switched linear systems are merged together to derive a…
We study the dynamical properties of a broad class of high-dimensional random dynamical systems exhibiting chaotic as well as fixed point and periodic attractors. We consider cases in which attractors can co-exists in some regions of the…
The universal mechanism resulting in the generalized synchronization regime arising in the chaotic oscillators with the dissipative coupling has been described. The reasons of the generalized synchronization occurrence may be clarified by…
Pulses of synchronization in chaotic coupled map lattices are discussed in the context of transmission of information. Synchronization and desynchronization propagate along the chain with different velocities which are calculated…
This paper is concerned with the stability analysis of continuous-time switched systems with a random switching signal. The switching signal manifests its characteristics with that the dwell time in each subsystem consists of a fixed part…