相关论文: Replication of Period-Doubling Route to Chaos in C…
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…
Task replication has recently been advocated as a practical solution to reduce latencies in parallel systems. In addition to several convincing empirical studies, some others provide analytical results, yet under some strong assumptions…
In this article we study networks of coupled dynamical systems with time-delayed connections. If two such networks hold different delays on the connections it is in general possible that they exhibit different dynamical behavior as well. We…
The appropriate selection of recurrence thresholds is a key problem in applications of recurrence quantification analysis (RQA) and related methods across disciplines. Here, we discuss the distribution of pairwise distances between state…
We review the occurrence of the patterns of the onset of chaos in low-dimensional nonlinear dissipative systems in leading topics of condensed matter physics and complex systems of various disciplines. We consider the dynamics associated…
Anticipated synchronisation occurs when a driven dynamical system synchronises with the future state of the driver system to which it is unidirectionally coupled. Previous theoretical and experimental studies have focused on setups with a…
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…
The renormalization method which is a type of perturbation method is extended to a tool to study weakly nonlinear time-delay systems. For systems with order-one delay, we show that the renormalization method leads to reduced systems without…
The possibility of realization of the phenomena of complex analytic dynamics for the realistic physical models are investigated. Observation of the Mandelbrot and Julia sets in the parameter and phase spaces both for the discrete maps and…
The time needed to exchange information in the physical world induces a delay term when the respective system is modeled by differential equations. Time delays are hence ubiquitous, being furthermore likely to induce instabilities and with…
Hybrid systems with memory refer to dynamical systems exhibiting both hybrid and delay phenomena. While systems of this type are frequently encountered in many physical and engineering systems, particularly in control applications, various…
We present a method for time series analysis of both, scalar and nonscalar time-delay systems. If the dynamics of the system investigated is governed by a time-delay induced instability, the method allows to determine the delay time. In a…
Distributed delay equations have been used to model situations in which there is some sort of delay whose duration is uncertain. However, the interpretation of a distributed delay equation is actually very different from that of a delay…
A general method for constructing simplicial complex from observed time series of dynamical systems based on the delay coordinate reconstruction procedure is presented. The obtained simplicial complex preserves all pertinent topological…
Recently, different approaches have been proposed for studying basic properties of time series from a complex network perspective. In this work, the corresponding potentials and limitations of networks based on recurrences in phase space…
Spatiotemporal chaos in the form of defect-mediated turbulence is known for oscillators coupled by diffusion. Here we explore the same conditions that produce defect turbulence, in an array of oscillators that are coupled through the…
Under some mild condition, a random walk in the plane is recurrent. In particular each trajectory is dense, and a natural question is how much time one needs to approach a given small neighborhood of the origin. We address this question in…
Nonlinear classical dissipative systems present a rich phenomenology in their "route to chaos", including period-doubling, i.e. the system evolves with a period which is twice that of the driving. However, typically the attractor of a…
In this manuscript, we study the problem of robust synchronization in networks of diffusively time-delayed coupled nonlinear systems. In particular, we prove that, under some mild conditions on the input-output dynamics of the systems and…
The linear response of synchronized chaotic units with delayed couplings and feedback to small external perturbations is investigated in the context of communication with chaos synchronization. For iterated chaotic maps, the distribution of…