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We study the regime of anticipated synchronization in unidirectionally coupled chaotic maps such that the slave map has its own output reinjected after a certain delay. For a class of simple maps, we give analytic conditions for the…
We introduce "state space persistence analysis" for deducing the symbolic dynamics of time series data obtained from high-dimensional chaotic attractors. To this end, we adapt a topological data analysis technique known as persistent…
In this work, we are interested in structure learning for a set of spatially distributed dynamical systems, where individual subsystems are coupled via latent variables and observed through a filter. We represent this model as a directed…
We introduce a new dynamical indicator of stability based on the Extreme Value statistics showing that it provides an insight on the local stability properties of dynamical systems. The indicator perform faster than other based on the…
This paper proposes Koopman operator theory and the related algorithm dynamical mode decomposition (DMD) for analysis and control of signalized traffic flow networks. DMD provides a model-free approach for representing complex oscillatory…
The aim of this paper is to rigorously study dynamics of Heterogeneously Coupled Maps (HCM). Such systems are determined by a network with heterogeneous degrees. Some nodes, called hubs, are very well connected while most nodes interact…
Collective behavior is studied in globally coupled maps with distributed nonlinearity. It is shown that the heterogeneity enhances regularity in the collective dynamics. Low-dimensional quasiperiodic motion is often found for the…
A new approach to analysis of the synchronization of chaotic oscillations in two (or more) coupled oscillators is described that makes it possible to reveal changes in the structure of attractors and detect the appearance of intermittency.…
The theory of slow manifolds is an important tool in the study of deterministic dynamical systems, giving a practical method by which to reduce the number of relevant degrees of freedom in a model, thereby often resulting in a considerable…
Symmetry properties of the evolution equation and the state to be controlled are shown to determine the basic features of the linear control of unstable orbits. In particular, the selection of control parameters and their minimal number are…
We study the dynamics of an ensemble of globally coupled chaotic logistic maps under the action of a learning algorithm aimed at driving the system from incoherent collective evolution to a state of spontaneous full synchronization.…
This paper presents a rigorous analytical model of traffic dynamics on a circular track, demonstrating the emergence of standing oscillations resulting from microscopic driver behaviour, delay responses, and proximity pressure. Without…
In this paper we investigate the growth rate of the number of all possible paths in graphs with respect to their length in an exact analytical way. Apart from the typical rates of growth, i.e. exponential or polynomial, we identify…
We consider a lattice of weakly coupled expanding circle maps. We construct, via a cluster expansion of the Perron-Frobenius operator, an invariant measure for these infinite dimensional dynamical systems which exhibits space-time-chaos.
Inspired by theories such as Loop Quantum Gravity, a class of stochastic graph dynamics was studied in an attempt to gain a better understanding of discrete relational systems under the influence of local dynamics. Unlabeled graphs in a…
This note aims to bring attention to a simple class of discrete dynamical systems exhibiting some complex behaviour. Each of these systems is defined as a self-mapping of the unit square and is obtained by coupling two families of…
This article proposes a novel methodology to learn a stable robot control law driven by dynamical systems. The methodology requires a single demonstration and can deduce a stable dynamics in arbitrary high dimensions. The method relies on…
This paper investigates the chaotic properties of Arnol'd cat maps (ACMs) coupled on the nodes of a circulant graph. By demanding that the system's evolution matrix be symplectic, we determine the coupling matrix, which is naturally…
We investigate a model of high-dimensional dynamical variables with all-to-all interactions that are random and non-reciprocal. We characterize its phase diagram and show that the model can exhibit chaotic dynamics. We show that the…
Symbolic models are abstract descriptions of continuous systems in which symbols represent aggregates of continuous states. In the last few years there has been a growing interest in the use of symbolic models as a tool for mitigating…