Chimera states: Effects of different coupling topologies

Collective behavior among coupled dynamical units can emerge in various forms as a result of different coupling topologies as well as different types of coupling functions. Chimera states have recently received ample attention as a fascinating manifestation of collective behavior, in particular describing a symmetry breaking spatiotemporal pattern where synchronized and desynchronized states coexist in a network of coupled oscillators. In this perspective, we review the emergence of different chimera states, focusing on the effects of different coupling topologies that describe the interaction network connecting the oscillators. We cover chimera states that emerge in local, nonlocal and global coupling topologies, as well as in modular, temporal and multilayer networks. We also provide an outline of challenges and directions for future research.Comment: 7 two-column pages, 4 figures; Perspective accepted for publication in EP

Characterization of synchronization spatiotemporal states in coupled non identical complex Ginzburg-Landau equations.

We characterize the synchronization of two nonidentical spatially extended elds ruled by onedimensional Complex Ginzburg{Landau equations, in the two regimes of phase and amplitude turbulence. If two elds display the same dynamical regime, the coupling induces a transition to a completely synchronized state. When, instead, the two elds are in di erent dynamical regimes, the transition to complete synchronization is mediated by defect synchronization. In the former case, the synchronized manifold is dynamically equivalent to that of the unsynchronized systems, while in the latter case the synchronized state substantially di ers from the unsynchronized one, and it is mainly dictated by the synchronization process of the space-time defects

Synchronization of spatially extended chaotic systems in the presence of asymmetric coupling

In a recent paper [Phys. Rev. Lett. 91, 064103 (2003)] we described the effects of asymmetric coupling configurations on the synchronization of spatially extended systems. In this paper, we report the consequences induced by the presence of asymmetries in the coupling scheme on the synchronization process of a pair of one-dimensional fields obeying complex Ginzburg-Landau equations. While synchronization always occurs for large enough coupling strengths, asymmetries have the effect of enhancing synchronization and play a crucial role in setting the threshold for the appearance of the synchronized dynamics, as well as in selecting the statistical and dynamical properties of the synchronized motion. We analyze the process of synchronization in the presence of asymmetries when the dynamics is affected by the presence of phase singularities, and show that defects tend to anchor one system to the other. In addition, asymmetry controls the number of synchronized defects that are present in the dynamics. Possible consequences of such asymmetry induced effects in biological and natural systems are discussed

Unified treatment of synchronization patterns in generalized networks with higher-order, multilayer, and temporal interactions

When describing complex interconnected systems, one often has to go beyond the standard network description to account for generalized interactions. Here, we establish a unified framework to simplify the stability analysis of cluster synchronization patterns for a wide range of generalized networks, including hypergraphs, multilayer networks, and temporal networks. The framework is based on finding a simultaneous block diagonalization (SBD) of the matrices encoding the synchronization pattern and the network topology. As an application, we use SBD to discover a novel type of chimera states that only appear in the presence of higher-order interactions. The unified framework established here can be extended to other dynamical processes and can facilitate the discovery of novel emergent phenomena in complex systems with generalized interactions

Synchronization Behavior in Coupled Chemical Oscillators

Synchronization is a collective phenomenon emerging from the interactions of different dynamical systems. Systems with different characteristics adjust their behavior to a common behavior of the group. This collective behavior is observed in many biological, chemical, and physical systems. Examples from different fields include pacemaker heart cells, synchronization of neurons during epilepsy seizures, arrays of microwave oscillators, and robot manipulators. Studies of coupled oscillators have revealed different mechanisms by which discrete oscillators interact and organize to a uniform synchronized state from an incoherent state. The discovery of a new type of synchronization state, called the chimera state has further broadened the field of synchronization. A chimera state is made up of coexisting subpopulations of oscillators, each with same coupling structure, but with one exhibiting synchronous behavior and the other asynchronous behavior. The phenomena has been the focus of much theoretical and experimental research in the past decade. In this thesis, experimental and simulation studies of chimera states in populations of coupled chemical oscillators will be described and their relation to other synchronization states will be characterized. Experiments were carried out with the photosensitive Belousov-Zhabotinsky (BZ) chemical oscillators and a light feedback scheme. The dimensionless two-variable Zhabotinsky-Buchholtz-Kiyatin-Epstein (ZBKE) model of the BZ chemical system was used in simulations.;A two-group coupling model, which splits the oscillators into two subpopulations, was used in the first part of the study. The subpopulations are globally coupled, both within and between the subpopulations. The coupling of every oscillator with members of the other subpopulation is weaker than the coupling with members of its own subpopulation. In-phase, out-of-phase, and phase-cluster synchronized states, as well as the chimera state, were found in both experiments and simulations. The probability of finding a chimera state decreases with increasing intra-group coupling strength. The study also revealed that heterogeneity in the frequencies of the oscillators in the system decreases the lifetime of a chimera. This was evidenced by the collapse of the chimera state to a synchronized state in both experiments and simulations with heterogeneous oscillators.;Synchronized and mixed-state behaviors are observed in populations of nonlocally coupled chemical oscillators in a ring configuration. With nonlocal coupling, the nearest neighbors are strongly coupled and the coupling strength decreases exponentially with distance. Experimental studies show stable chimera states, phase cluster states and phase waves coexisting with unsychronized groups of oscillators. These are spontaneously formed from quasi-random initial phase distributions in the experiments and random initial phase distributions in simulations. Simulations with homogeneous and heterogeneous oscillators revealed that a finite spread of frequencies increases the probability of initiating a synchronized group, leading to chimera states. The effects of group size and coupling strength on chimera states, phase waves, phase clusters, and traveling waves are discussed. Complex behaviors in coexisting states were analyzed, consisting of periodic phase slips with identical oscillators and periodic switching with nonidentical oscillators. Fourier transform analysis was used to distinguish between states exhibiting high periodicity and chimera states, which show similar average behavior

Instabilities, pattern formation, localized solutions, mode-locking and stochastic effects in nonlinear optical systems and beyond

In this thesis the results of scientific research about dierent nonlinear phenomena with particular emphasis to photonic systems are presented. Works about dissipation induced modulation instabilities with applications for signal amplification in nonlinear optics and mode-locking in lasers constitute the main part of the thesis. The dissipa-tive instabilities studied are of two kinds, parametric instabilities induced by a periodic variation of spectral losses and instabilities induced by non varying but spectrally asym-metric losses. Although the main achievements are theoretical successful collaboration with experimentalists are reported too. Other results presented in this thesis concern a new fundamental theory of active mode-locking in lasers having a more general validity than Haus’ one and hence useful for describing mode-locked lasers with a fast gain dynamics such as semiconductor or quantum cascade lasers; the prediction of the novel theoretical model have been successfully compared with experimental findings. Theo-retical studies are also presented about collective phenomena, such as synchronization and localization, in coupled excitable lasers with saturable absorber and localized so-lutions on the non-vanishing background of the two-dimensional nonlinear Schr¨odinger equation with periodic potential: the Bogoliubov-de Gennes bullets

Adomian decomposition method, nonlinear equations and spectral solutions of burgers equation

Tese de doutoramento. Ciências da Engenharia. 2006. Faculdade de Engenharia. Universidade do Porto, Instituto Superior Técnico. Universidade Técnica de Lisbo