Related papers: Transition from anticipatory to lag synchronizatio…
Many biological systems can sense periodical variations in a stimulus input and produce well-timed, anticipatory responses after the input is removed. Such systems show memory effects for retaining timing information in the stimulus and…
Transitions to measure synchronization in two coupled $\phi ^{4}$ lattices are investigated based on numerical simulations. The relationship between measure synchronization (MS), phase locking and system's total energy is studied both for…
We investigate synchronization in the presence of delay time modulation for application to communication. We have observed that the robust synchronization is established by a common delay signal and its threshold is presented using Lyapunov…
In finite-dimensional, chaotic, Lorenz-like wave-particle dynamical systems one can find diffusive trajectories, which share their appearance with that of laminar chaotic diffusion [Phys. Rev. Lett. 128, 074101 (2022)] known from delay…
This paper studies how complicated and irregular behavior, known as chaos, can arise in a simple mathematical model that includes time delays. The model is a delay differential equation in which the present rate of change depends not only…
Numerical experiments recently discussed in the literature show that identical nonlinear chaotic systems linked by a common noise term (or signal) may synchronize after a finite time. We study the process of synchronization as function of…
We present the first report on chaos synchronization between two unidirectionally linearly and nonlinearly coupled systems with multiple time-delays and using the Razumikhin-Lyapunov approach find the existence and stability conditions for…
Synchronization in a group of linear time-invariant systems is studied where the coupling between each pair of systems is characterized by a different output matrix. Simple methods are proposed to generate a (separate) linear coupling gain…
Synchronization is studied in an array of identical oscillators undergoing small vibrations. The overall coupling is described by a pair of matrix-weighted Laplacian matrices; one representing the dissipative, the other the restorative…
We analyse universal statistical properties of phase shifts and time delays for open chaotic systems in the crossover regime of partly broken time-reversal invariance. In particular, we find that the distribution of the time delay shows…
This paper deals with the chaotic oscillator synchronization. A new approach to the synchronization of chaotic oscillators has been proposed. This approach is based on the analysis of different time scales in the time series generated by…
Synchronization is an omnipresent collective phenomenon in nature and technology, whose understanding is in particular for real-world systems still elusive. We study the synchronization transition in a phase oscillator system with two…
In this paper, we characterize the synchronization phenomenon of hyperchaotic scalar non-linear delay dynamics in a fully-developed chaos regime. Our results rely on the observation that, in that regime, the stationary statistical…
Phase synchronization is shown to occur between opposite cells of a ring consisting of chaotic Lorenz oscillators coupled unidirectionally through driving. As the coupling strength is diminished, full phase synchronization cannot be…
We investigate the dynamics of an array of logistic maps coupled with random delay times. We report that for adequate coupling strength the array is able to synchronize, in spite of the random delays. Specifically, we find that the…
A new approach is proposed to the integrated analysis of the time structure of synchronization of multidimensional chaotic systems. The method allows one to diagnose and quantitatively evaluate the intermittency characteristics during…
By studying laser systems with multiple time delays, we demonstrate that the signatures of time delays in the autocorrelation coefficient and the mutual information of the laser output can be erased for systems with variable time delays.…
Dynamical systems with complex delayed interactions arise commonly when propagation times are significant, yielding complicated oscillatory instabilities. In this Letter, we introduce a class of systems with multiple, hierarchically long…
We consider the effect of asymmetric temporal delays in a system of two coupled Hopfield neurons. For couplings of opposite signs, a limit cycle emerges via a supercritical Hopf bifurcation when the sum of the delays reaches a critical…
Circular D0L-systems are those with finite synchronizing delay. We introduce a tool called graph of overhangs which can be used to find the minimal value of synchronizing delay of a given D0L-system. By studying the graphs of overhangs, a…