Related papers: Pattern Formation in Excitable Neuronal Maps
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…
In this paper we present a rigorous analysis of a class of coupled dynamical systems in which two distinct types of components, one excitatory and the other inhibitory, interact with one another. These network models are finite in size but…
This is a significantly expanded version of the survey paper "Mixing and decay of correlations in non-uniformly expanding maps: a survey of recent results" math/0301319. We discuss recent results on decay of correlations for non-uniformly…
The coherence of two, coupled two-level systems, representing vibrational modes in a semiclassical model, is calculated in weak and strong fields for various coupling schemes and for different relative phases between initial state…
We analyse the stochastic dynamics of a bistable system under the influence of time-delayed feedback. Assuming an asymmetric potential, we show the existence of a regime in which the systems dynamic displays excitability by calculating the…
The gravitational wave signals produced by the coalescence of compact binaries progress through three stages: inspiral, merger, and postmerger. The evolution of their frequency follows a slow build up during the inspiral that peaks at…
We investigated the dynamical behaviors of bimodular continuous attractor neural networks, each processing a modality of sensory input and interacting with each other. We found that when bumps coexist in both modules, the position of each…
This chapter revisits the concept of excitability, a basic system property of neurons. The focus is on excitable systems regarded as behaviors rather than dynamical systems. By this we mean open systems modulated by specific interconnection…
We present extensive numerical investigations on the ergodic properties of two identical Pomeau-Manneville maps interacting on the unit square through a diffusive linear coupling. The system exhibits anomalous statistics, as expected, but…
We study a prototypical model of two coupled two-level systems, where the competition between coherent and dissipative coupling gives rise to a rich phenomenology. In particular, we analyze the case of asymmetric coupling, as well as the…
The most general form of a marginal extended perturbation in a two-dimensional system is deduced from scaling considerations. It includes as particular cases extended perturbations decaying either from a surface, a line or a point for which…
Rhythmic and sequential segmentation of the embryonic body plan is a vital developmental patterning process in all vertebrate species. However, a theoretical framework capturing the emergence of dynamic patterns of gene expression from the…
We investigate a possibility of realization of structurally stable chaotic dynamics in neural systems. The considered model of interacting neurons consists of a pair of coupled FitzHugh-Nagumo systems, with the parameters being periodically…
We present simulations of peak pattern formation in vibrated two-dimensional (2D) granulates and measure the dispersion relation of the pattern for various frequencies, accelerations, cell sizes, and layer heights. We report the first…
Pattern formation often occurs in spatially extended physical, biological and chemical systems due to an instability of the homogeneous steady state. The type of the instability usually prescribes the resulting spatio-temporal patterns and…
We analyze the physical mechanisms leading either to synchronization or to the formation of spatio-temporal patterns in a lattice model of pulse-coupled oscillators. In order to make the system tractable from a mathematical point of view we…
Compliant environments can mediate interactions between mechanically active cells like fibroblasts. Starting with a phenomenological model for the behaviour of single cells, we use extensive Monte Carlo simulations to predict non-trivial…
In this paper, we study pairs of oscillators that are indirectly coupled via active (excitable) cells. We introduce a scalar phase model for coupled oscillators and excitable cells. We first show that one excitable and one oscillatory cell…
It has been reported that traveling waves propagate periodically and stably in sub-excitable systems driven by noise [Phys. Rev. Lett. \textbf{88}, 138301 (2002)]. As a further investigation, here we observe different types of traveling…
Pattern separation is a computational process by which dissimilar neural patterns are generated from similar input patterns. We present an information-geometric formulation of pattern separation, where a pattern separator is modelled as a…