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Lagrangian transport structures for three-dimensional and time-dependent fluid flows are of great interest in numerous applications, particularly for geophysical or oceanic flows. In such flows, chaotic transport and mixing can play…
Transitive consistency is an intrinsic property for collections of linear invertible transformations between Euclidean coordinate frames. In practice, when the transformations are estimated from data, this property is lacking. This work…
We experimentally demonstrate the occurrence of various synchronized states in coupled piece-wise linear time-delayed electronic circuits using dynamic environment coupling where the environment has its own intrinsic dynamics via feedback…
The content of this contribution is based on the course on numerical analysis techniques for non-linear dynamics. After introducing basic concepts as the visual analysis of trajectories in phase space and the importance of the nature of…
We describe a flexible and modular delayed-feedback nonlinear oscillator that is capable of generating a wide range of dynamical behaviours, from periodic oscillations to high-dimensional chaos. The oscillator uses electrooptic modulation…
Two numerical methods are proposed for detection of coupling between multiple time series generated by deterministic nonlinear systems. The first detects interdependence or the existence of coupling between time series. The second…
This work redefines the framework of chaos in dynamical systems by extending Devaney's definition to multiple mappings, emphasizing the pivotal role of nonlinearity. We propose a novel theorem demonstrating how nonlinear dynamics within a…
Traveling waves triggered by a phase slip in coupled map lattices are studied. A local phase slip affects globally the system, which is in strong contrast with kink propagation. Attractors with different velocities coexist, and form…
The problem of synchronization in heterogeneous networks of linear systems with nonlinear delayed diffusive coupling is considered. The network is presented in new coordinates mean-field dynamics and synchronization errors. Thus the problem…
Understanding how nonequilibrium systems respond to perturbations is a central challenge in physics. In this work, we establish mutual linearity in nonequilibrium overdamped Langevin systems. This theory provides a framework for controlling…
The phase ordering dynamics of coupled chaotic maps on fractal networks are investigated. The statistical properties of the systems are characterized by means of the persistence probability of equivalent spin variables that define the…
The dynamics of transitional flows are governed by an interplay between the non-normal linear dynamics and quadratic nonlinearity in the incompressible Navier-Stokes equations. In this work, we propose a framework for nonlinear stability…
The present paper explores the synchronization scenario of hyperchaotic time-delayed electronic oscillators coupled indirectly via a common environment. We show that depending upon the coupling parameters a hyperchaotic time-delayed system…
Coupled oscillator networks often display transitions between qualitatively different phase-locked solutions -- such as synchrony and rotating wave solutions -- following perturbation or parameter variation. In the limit of weak coupling,…
In presence of unstable dimension variability numerical solutions of chaotic systems are valid only for short periods of observation. For this reason, analytical results for systems that exhibit this phenomenon are needed. Aiming to go one…
We review our recent work on the synchronization of a network of delay-coupled maps, focusing on the interplay of the network topology and the delay times that take into account the finite velocity of propagation of interactions. We assume…
Synchronized chaos has previously been predicted and observed in a small number (3) of mutually coupled lasers. In this work, we demonstrate that this phenomenon can theoretically persist in significantly broader scenarios, extending to…
We focus on chaotic dynamical systems and analyze their time series with the use of autoencoders, i.e., configurations of neural networks that map identical output to input. This analysis results in the determination of the latent space…
Auxiliary system approach and various nearest neighbor methods are widely used to detect generalized synchronization in non-identical coupled systems. These methods generally give contradictory results. Therefore one method alone is not…
The behaviors of coupled chaotic oscillators before complete synchronization were investigated. We report three phenomena: (1) The emergence of long-time residence of trajectories besides one of the saddle foci; (2) The tendency that orbits…