Related papers: Spectral Properties and Synchronization in Coupled…
In the study of dynamical systems on networks/graphs, a key theme is how the network topology influences stability for steady states or synchronized states. Ideally, one would like to derive conditions for stability or instability that…
Coupled Map Lattice (CML) models are particularly suitable to study spatially extended behaviours, such as wave-like patterns, spatio-temporal chaos, and synchronisation. Complete synchronisation in CMLs emerges when all maps have their…
We study the spatially synchronized and temporally periodic solutions of a 1-d lattice of coupled sine circle maps. We carry out an analytic stability analysis of this spatially synchronized and temporally periodic case and obtain the…
We study two problems related to spatially extended systems: the dynamical stability and the universality classes of the replica synchronization transition. We use a simple model of one dimensional coupled map lattices and show that chaotic…
We show that the threshold of complete synchronization in a lattice of coupled non-smooth chaotic maps is determined by linear stability along the directions transversal to the synchronization subspace. As a result, the numerically…
In the realm of spatiotemporal chaos, unstable periodic orbits play a major role in understanding the dynamics. Their stability changes and bifurcations in general are thus of central interest. Here, coupled map lattice discretizations of…
In recent years, information security essential in various arenas like internet communication, multimedia systems, medical imaging, tele-medicine and military communication. However, most of them faced with some problems such as the lack of…
Recent studies in ecology and epidemiology indicate that it is important to include spatial heterogeneity, synchronization and seasonality in the theoretical models. In this work, spatial heterogeneity is introduced via coupled map lattices…
Linear control theory is used to develop an improved localized control scheme for spatially extended chaotic systems, which is applied to a Coupled Map Lattice as an example. The optimal arrangement of the control sites is shown to depend…
Coupled map lattices (CMLs) are often used to study emergent phenomena in nature. It is typically assumed (unrealistically) that each component is described by the same map, and it is important to relax this assumption. In this paper, we…
In this work we consider two models of two dimensional discrete systems subjected to three different types of coupling and analyse systematically the performance of each in realising synchronised states.We find that linear coupling…
We obtain exact analytical results for lattices of maps with couplings that decay with distance as $r^{-\alpha}$. We analyze the effect of the coupling range on the system dynamics through the Lyapunov spectrum. For lattices whose elements…
We consider the stability of synchronized states (including equilibrium point, periodic orbit or chaotic attractor) in arbitrarily coupled dynamical systems (maps or ordinary differential equations). We develop a general approach, based on…
This paper presents an application of partial contraction analysis to the study of global synchronization in discrete chaotic systems. Explicit sufficient conditions on the coupling strength of networks of discrete oscillators are derived.…
We locate gaps in the spectrum of a Hamiltonian on a periodic cuboidal (and generally hyperrectangular) lattice graph with $\delta$ couplings in the vertices. We formulate sufficient conditions under which the number of gaps is finite. As…
We study some spectral properties of a matrix that is constructed as a combination of a Laplacian and an adjacency matrix of simple graphs. The matrix considered depends on a positive parameter, as such we consider the implications in…
We investigate the spectral properties of chaotic quantum graphs. We demonstrate that the `energy'--average over the spectrum of individual graphs can be traded for the functional average over a supersymmetric non--linear $\sigma$--model…
We illustrate, through a series of prototypical examples, that linear parity-time (PT) symmetric lattices with extended gain/loss profiles are generically unstable, for any non-zero value of the gain/loss coefficient. Our examples include a…
We show that the dynamical behavior of a coupled map lattice where the individual maps are Bernoulli shift maps can be solved analytically for integer couplings. We calculate the invariant density of the system and show that it displays a…
We study operators on rooted graphs with a certain spherical homogeneity. These graphs are called path commuting and allow for a decomposition of the adjacency matrix and the Laplacian into a direct sum of Jacobi matrices which reflect the…