Related papers: Symbolic dynamics and synchronization of coupled m…
Differential equations are a ubiquitous tool to study dynamics, ranging from physical systems to complex systems, where a large number of agents interact through a graph with non-trivial topological features. Data-driven approximations of…
This paper deals with adaptive synchronization of chaos in the presence of time-varying communication-delays. We consider two bidirectionally coupled systems that seek to synchronize through a signal that each system sends to the other one…
Synchronization is a crucial phenomenon in many natural and artificial complex network systems. Applications include neuronal networks, formation control and coordination in robotics, and frequency synchronization in electrical power grids.…
Physical dynamic networks most commonly consist of interconnections of physical components that can be described by diffusive couplings. These diffusive couplings imply that the cause-effect relationships in the interconnections are…
We study systems of identical coupled oscillators introducing a distribution of delay times in the coupling. For arbitrary network topologies, we show that the frequency and stability of the fully synchronized states depend only on the mean…
Synchronization of chaotic units coupled by their time delayed variables are investigated analytically. A new type of cooperative behavior is found: sublattice synchronization. Although the units of one sublattice are not directly coupled…
Time-delay systems are, in many ways, a natural set of dynamical systems for natural scientists to study because they form an interface between abstract mathematics and data. However, they are complicated because past states must be…
Interpretable mathematical expressions defining discrete-time dynamical systems (iterated maps) can model many phenomena of scientific interest, enabling a deeper understanding of system behaviors. Since formulating governing expressions…
We study the synchronization of two chaotic maps with unidirectional (master-slave) coupling. Both maps have an intrinsic delay $n_1$, and coupling acts with a delay $n_2$. Depending on the sign of the difference $n_1-n_2$, the slave map…
The detection of phase synchronization of coupled chaotic oscillators which are not phase-coherent is known to be a challenging task. In this work a method to detect and measure phase synchronization is presented. The procedure uses symbol…
We introduce an analytical approach that allows predictions and mechanistic insights into the dynamics of nonlinear oscillator networks with heterogeneous time delays. We demonstrate that time delays shape the spectrum of a matrix…
For the first time, using a modified Ikeda model it is demonstrated analytically that anticipating synchronization can be obtained in chaotic time-delay systems governed by two characteristic delay times. We derive existence and stability…
Topological signals, i.e., dynamical variables defined on nodes, links, triangles, etc. of higher-order networks, are attracting increasing attention. However the investigation of their collective phenomena is only at its infancy. Here we…
This paper studies the construction of symbolic abstractions for nonlinear control systems via feedback refinement relation. Both the delay-free and time-delay cases are addressed. For the delay-free case, to reduce the computational…
Visibility algorithms transform time series into graphs and encode dynamical information in their topology, paving the way for graph-theoretical time series analysis as well as building a bridge between nonlinear dynamics and network…
Existence of a new type of oscillating synchronization that oscillates between three different types of synchronizations (anticipatory, complete and lag synchronizations) is identified in unidirectionally coupled nonlinear time-delay…
Spatially extended dynamical systems, namely coupled map lattices, driven by additive spatio-temporal noise are shown to exhibit stochastic synchronization. In analogy with low-dymensional systems, synchronization can be achieved only if…
At an unmanaged intersection, it is important to understand how much traffic delay may be caused as a result of microscopic vehicle interactions. Conventional traffic simulations that explicitly track these interactions are time-consuming.…
A single dynamical system with time-delayed feedback can emulate networks. This property of delay systems made them extremely useful tools for Machine Learning applications. Here we describe several possible setups, which allow emulating…
We propose an algorithm for the detection of recurrence domains of complex dynamical systems from time series. Our approach exploits the characteristic checkerboard texture of recurrence domains exhibited in recurrence plots (RP). In phase…