相关论文: Coupled Maps on Trees

A unified approach for analyzing synchronization in coupled systems of autonomous differential equations is presented in this work. Through a careful analysis of the variational equation of the coupled system we establish a sufficient…

A mean-field formulation is used to investigate the bifurcation diagram for globally coupled tent maps by means of an analytical approach. It is shown that the period doubling sequence of the single site map induces a continuous family of…

We introduce and explore patterned lattices consisting of coupled isospectral cells that vary across the lattice. The isospectrality of the cells is encapsulated in the phase that characterizes each cell and can be designed at will such…

We study the influence of network topology and connectivity on the synchronization properties of chaotic logistic maps, interacting with random delay times. Four different types of topologies are investigated: two regular (a ring-type and a…

Networks of chaotic units with static couplings can synchronize to a common chaotic trajectory. The effect of dynamic adaptive couplings on the cooperative behavior of chaotic networks is investigated. The couplings adjust to the activities…

There are three key factors of a system of coupled oscillators that characterize the interaction among them: coupling (how to affect), delay (when to affect) and topology (whom to affect). For each of them, the existing work has mainly…

It is shown how different globally coupled map systems can be analyzed under a common framework by focusing on the dynamics of their respective global coupling functions. We investigate how the functional form of the coupling determines the…

We prove a number of identities relating the sofic entropy of a certain class of non-expansive algebraic dynamical systems, the sofic entropy of the Wired Spanning Forest and the tree entropy of Cayley graphs of residually finite groups. We…

Coupled map lattices (CMLs) are prototypical dynamical systems on networks/graphs. They exhibit complex patterns generated via the interplay of diffusive/Laplacian coupling and nonlinear reactions modelled by a single iterated map at each…

Complexity of dynamical networks can arise not only from the complexity of the topological structure but also from the time evolution of the topology. In this paper, we study the synchronous motion of coupled maps in time-varying complex…

In this work, we consider 2D $\mathbb{Z}_2$ topologically ordered phases ($\mathbb{Z}_2$ toric code and the modified surface code) on a simple hyperbolic lattice. Introducing a 2D lattice consisting of the product of a 1D Cayley tree and a…

We study the stability of the fixed-point solution of an array of mutually coupled logistic maps, focusing on the influence of the delay times, $\tau_{ij}$, of the interaction between the $i$th and $j$th maps. Two of us recently reported…

Synchronization of coupled harmonic oscillators is investigated. Coupling considered here is pairwise, unidirectional, and described by a nonlinear function (whose graph resides in the first and third quadrants) of some projection of the…

We investigate the synchronization phenomenon in coupled chaotic map lattices where the couplings decay with distance following a power-law. Depending on the lattice size, the coupling strength and the range of the interactions, complete…

We consider the pattern formation problem in coupled identical systems after the global synchronized state becomes unstable. Based on analytical results relating the coupling strengths and the instability of each spatial mode (pattern) we…

We describe a simple adaptive network of coupled chaotic maps. The network reaches a stationary state (frozen topology) for all values of the coupling parameter, although the dynamics of the maps at the nodes of the network can be…

We study effects of delay in diffusively coupled logistic maps on the Cayley tree networks. We find that smaller coupling values exhibits sensitiveness for value of delay, and leads to different cluster patterns of self-organized and driven…

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…

Bifurcations in a system of coupled maps are investigated. Using symbolic dynamics it is proven that for coupled shift maps the well known space--time--mixing attractor becomes unstable at a critical coupling strength in favour of a…

Synchronization control in arrays of identical output-coupled continuous-time linear systems is studied. Sufficiency of new conditions for the existence of a synchronizing feedback law are analyzed. It is shown that for neutrally stable…