Related papers: Applied Symbolic Vector Dynamics of Coupled Map La…
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…
A variety of complex fluids under shear exhibit complex spatio-temporal behaviour, including what is now termed rheological chaos, at moderate values of the shear rate. Such chaos associated with rheological response occurs in regimes where…
A model of interacting motile chaotic elements is proposed. The chaotic elements are distributed in space and interact with each other through interactions depending on their positions and their internal states. As the value of a governing…
By choosing a dynamical system with d different couplings, one can rearrange a system based on the graph with given vertex dependent on the dynamical system elements. The relation between the dynamical elements (coupling) is replaced by a…
We revisit the globally coupled map lattice (GCML) and also propose a new extended globally coupled map lattice (EGCML) with an inverse power law interaction. In GCML we clarify the mechanism of the basic posi-nega switch in the two-cluster…
An array system of coupled maps is proposed as a model for economy evolution. The local dynamics of each map or agent is controlled by two parameters. One of them represents the growth capacity of the agent and the other one is a control…
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…
In this paper we study in detail, both analytically and numerically, the dynamical properties of the triangle map, a piecewise parabolic automorphism of the two-dimensional torus, for different values of the two independent parameters…
We study ergodic properties of a family of traffic maps acting in the space of bi-infinite sequences of real numbers. The corresponding dynamics mimics the motion of vehicles in a simple traffic flow, which explains the name. Using…
In this article, we continue the structural study of factor maps betweeen symbolic dynamical systems and the relative thermodynamic formalism. Here, one is studying a factor map from a shift of finite type $X$ (equipped with a potential…
We study coupled dynamics on networks using symbolic dynamics. The symbolic dynamics is defined by dividing the state space into a small number of regions (typically 2), and considering the relative frequencies of the transitions between…
The phenomenon of turbulence is investigated in the context of globally coupled maps. The local dynamics is given by the Chat\'e-Manneville minimal map previously used in studies of spatiotemporal intermittency in locally coupled map…
We present a new method of analysis of measure-preserving dynamical systems, based on frequency analysis and ergodic theory, which extends our earlier work [1]. Our method employs the novel concept of harmonic time average [2], and is…
Biological organisms must learn how to control their own bodies to achieve deliberate locomotion, that is, predict their next body position based on their current position and selected action. Such learning is goal-agnostic with respect to…
General hierarchical lattices of coupled maps are considered as dynamical systems. These models may describe many processes occurring in heterogeneous media with tree-like structures. The transition to turbulence via spatiotemporal…
We study expanding circle maps interacting in a heterogeneous random network. Heterogeneity means that some nodes in the network are massively connected, while the remaining nodes are only poorly connected. We provide a probabilistic…
In this paper we propose an elementary topological approach which unifies and extends various different results concerning fixed points and periodic points for maps defined on sets homeomorphic to rectangles embedded in euclidean spaces. We…
Iterations of odd piecewise continuous maps with two discontinuities, i.e., symmetric discontinuous bimodal maps, are studied. Symbolic dynamics is introduced. The tools of kneading theory are used to study the homology of the discrete…
A coupled map lattice whose topology changes at each time step is studied. We show that the transversal dynamics of the synchronization manifold can be analyzed by the introduction of effective dynamical quantities. These quantities are…
I introduce a novel mathematical framework integrating topological dynamics, operator algebras, and ergodic geometry to study lattices of asynchronous metric dynamical systems. Each node in the lattice carries an internal flow represented…