Related papers: Structure of Complex-Periodic and Chaotic Media wi…
The structure of spiral waves is investigated in super-excitable reaction-diffusion systems where the local dynamics exhibits multi-looped phase space trajectories. It is shown that such systems support stable spiral waves with broken…
Spiral waves are investigated in chemical systems whose underlying spatially-homogeneous dynamics is governed by a deterministic chaotic attractor. We show how the local periodic behavior in the vicinity of a spiral defect is transformed to…
Spiral waves are striking self-organized coherent structures that organize spatio-temporal dynamics in dissipative, spatially extended systems. In this paper, we provide a conceptual approach to various properties of spiral waves. Rather…
A spiral wave is a macroscopic dynamic of excitable media that plays an important role in several distinct systems, including the Belousov-Zhabotinsky reaction, seizures in the brain, and lethal arrhythmia in the heart. Because spiral wave…
Rotating spiral waves with a central core composed of phase-randomized oscillators can arise in reaction-diffusion systems if some of the chemical components involved are diffusion-free. This peculiar phenomenon is demonstrated for a…
Spiral waves are investigated in oscillatory media exhibiting period-doubling bifurcations. In the period-doubled and chaotic regimes, the rotational symmetry of the spiral wave is broken. The loss of symmetry takes the form of…
Excitable media are a generic class of models used to simulate a wide variety of natural systems including cardiac tissue. Propagation of excitation waves in this medium results in the formation of characteristic patterns such as rotating…
We identify a new type of pattern formation in spatially distributed active systems. We simulate one-dimensional two-component systems with predator-prey local interaction and pursuit-evasion taxis between the components. In a sufficiently…
The transition from complex-periodic to chaotic behavior is investigated in oscillatory media supporting spiral waves. We find turbulent regimes characterized by the spontaneous nucleation, proliferation and erratic motion of…
We study the drift of spiral waves in a simple model of heterogeneous excitable medium, having gradients in local excitability or cellular coupling. For the first time, we report the anomalous drift of spiral waves towards regions having…
Trapping and un-trapping of spiral tips in a two-dimensional homogeneous excitable medium with local small-world connections is studied by numerical simulation. In a homogeneous medium which can be simulated with a lattice of regular…
From cytoskeletal networks to tissues, many biological systems behave as active materials. Their composition and stress-generation is affected by chemical reaction networks. In such systems, the coupling between mechanics and chemistry…
We study a reaction diffusion system of the activator-inhibitor type with inhomogeneous reaction terms showing spatiotemporal chaos. We analyze the topological properties of the unstable periodic orbits in the slow chaotic dynamics…
Spiral waves are spatial-temporal patterns that can emerge in different systems as heart tissues, chemical oscillators, ecological networks and the brain. These waves have been identified in the neocortex of turtles, rats, and humans,…
We study the role of asymptotic curves in supporting the spiral structure of a N-body model simulating a barred spiral galaxy. Chaotic orbits with initial conditions on the unstable asymptotic curves of the main unstable periodic orbits…
The processes in nonequilibrium dissipative media caused by coherent structure formation and lead to the complicated dynamics are of interest for nonlinear physics. Here we consider a model of the flow of interacting electronics patterns.…
Spatiotemporal chaos in the form of defect-mediated turbulence is known for oscillators coupled by diffusion. Here we explore the same conditions that produce defect turbulence, in an array of oscillators that are coupled through the…
Biological and physical systems that can be classified as oscillatory media give rise to interesting phenomena like target patterns and spiral waves. The existence of these structures has been proven in the case of systems with local…
Spiral waves are ubiquitous in two-dimensional systems of chemical or biological oscillators coupled locally by diffusion. At the center of such spirals is a phase singularity, a topological defect where the oscillator amplitude drops to…
Spatio-temporal network dynamics is an emergent property of many complex systems which remains poorly understood. We suggest a new approach to its study based on the analysis of dynamical motifs -- small subnetworks with periodic and…