Related papers: Pattern Formation in Excitable Neuronal Maps

Chimera states, marked by the coexistence of order and disorder in systems of coupled oscillators, have captivated researchers with their existence and intricate patterns. Despite ongoing advances, a fully understanding of the genesis of…

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…

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…

We investigated the effect of time delays on phase configurations in a set of two-dimensional coupled phase oscillators. Each oscillator is allowed to interact with its neighbors located within a finite radius, which serves as a control…

We discuss synchronization patterns in networks of FitzHugh-Nagumo and Leaky Integrate-and-Fire oscillators coupled in a two-dimensional toroidal geometry. Common feature between the two models is the presence of fast and slow dynamics, a…

Recordings of increasingly large neural populations have revealed that the firing of individual neurons is highly coordinated. When viewed in the space of all possible patterns, the collective activity forms non-linear structures called…

Two-dimensional mappings obtained by coupling two piecewise increasing expanding maps are considered. Their dynamics is described when the coupling parameter increases in the expanding domain. By introducing a coding and by analysing an…

We study the dynamics and patterning of polar contractile filaments on the surface of a cylindrical cell using active hydrodynamic equations that incorporate couplings between curvature and filament orientation. Cables and rings…

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…

We study spatio-temporal pattern formation in a ring of N oscillators with inhibitory unidirectional pulselike interactions. The attractors of the dynamics are limit cycles where each oscillator fires once and only once. Since some of these…

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…

In recent years, the study of coupled excitable oscillators has largely benefited from a new analytical technique developed by Ott and Antonsen. This technique allows to express the dynamics of certain macroscopic observable in the ensemble…

Many natural systems including the brain comprise coupled non-uniformly stimulated elements. In this paper we show that heterogeneously driven networks of excitatory-inhibitory units exhibit striking collective phenomena, including…

We study the topological dynamics by iterations of a piecewise continuous, non linear and locally contractive map in a real finite dimensional compact ball. We consider those maps satisfying the "separation property": different continuity…

Numerical simulations of a simple reaction--diffusion model reveal a surprising variety of irregular spatio--temporal patterns. These patterns arise in response to finite--amplitude perturbations. Some of them resemble the steady irregular…

In a previous paper, we examined a class of possible conformations for helically patterned filaments in contact with a bonding surface. In particular, we investigated geometries where contact between the pattern and the surface was improved…

We study extremely diluted spin models of neural networks in which the connectivity evolves in time, although adiabatically slowly compared to the neurons, according to stochastic equations which on average aim to reduce frustration. The…

Systems of coupled oscillators have been seen to exhibit chimera states, i.e. states where the system splits into two groups where one group is phase locked and the other is phase randomized. In this work, we report the existence of chimera…

The paper examines the discrete-time dynamics of neuron models (of excitatory and inhibitory types) with piecewise linear activation functions, which are connected in a network. The properties of a pair of neurons (one excitatory and the…

Differentiable conjugacies link dynamical systems that share properties such as the stability multipliers of corresponding orbits. It provides a stronger classification than topological conjugacy, which only requires qualitative similarity.…