Related papers: Pattern Formation in Excitable Neuronal Maps

Excitable media are ubiquitous in nature, and in such systems the local excitation tends to self-organize in traveling waves, or in rotating spiral-shaped patterns in two or three spatial dimensions. Examples include waves during a pandemic…

We report on self-induced switchings between multiple distinct space--time patterns in the dynamics of a spatially extended excitable system. These switchings between low-amplitude oscillations, nonlinear waves, and extreme events strongly…

This research investigates the complex spatiotemporal behaviors of Chialvo neuron maps under the influence of Levy noise on three different network topologies that is a ring network, a two dimensional lattice affected by electromagnetic…

It is proposed that the spatial (and temporal) patterns spontaneously appearing in dissipative systems maximize the energy flow through the pattern forming interface. In other words - the patterns maximize the entropy growth rate in an…

We study the nonlinear dynamics of two delay-coupled neural systems each modelled by excitable dynamics of FitzHugh-Nagumo type and demonstrate that bistability between the stable fixed point and limit cycle oscillations occurs for…

Spiral waves in excitable media possess both wave-like and particle-like properties. When resonantly forced (forced at the spiral rotation frequency) spiral cores travel along straight trajectories, but may reflect from medium boundaries.…

Two-dimensional coupled map lattices have global stability properties that depend on the coupling between individual maps and their neighborhood. The action of the neighborhood on individual maps can be implemented in terms of "causal"…

Neural network models comprising elements which have exclusively excitatory or inhibitory synapses are capable of a wide range of dynamic behavior, including chaos. In this paper, a simple excitatory-inhibitory neural pair, which forms the…

Dynamical systems with complex delayed interactions arise commonly when propagation times are significant, yielding complicated oscillatory instabilities. In this Letter, we introduce a class of systems with multiple, hierarchically long…

In networked systems, the interplay between the dynamics of individual subsystems and their network interactions has been found to generate multistability in various contexts. Despite its ubiquity, the specific mechanisms and ingredients…

We study a simple map as a minimal model of excitable cells. The map has two fast variables which mimic the behavior of class I neurons, undergoing a sub-critical Hopf bifurcation. Adding a third slow variable allows the system to present…

The attractors of a dynamical system govern its typical long-term behaviour. The presence of many attractors is significant as it means the behaviour is heavily dependent on the initial conditions. To understand how large numbers of…

Local patterns of excitation and inhibition that can generate neural waves are studied as a computational mechanism underlying the organization of neuronal tunings. Sparse coding algorithms based on networks of excitatory and inhibitory…

Pattern forming systems allow for a wealth of states, where wavelengths and orientation of patterns varies and defects disrupt patches of monocrystalline regions. Growth of patterns has long been recognized as a strong selection mechanism.…

We introduce and solve a model which considers two coupled networks growing simultaneously. The dynamics of the networks is governed by the new arrival of network elements (nodes) making preferential attachments to pre-existing nodes in…

Spin chains with open boundaries, such as the transverse field Ising model, can display coherence times for edge spins that diverge with the system size as a consequence of almost conserved operators, the so-called strong zero modes. Here,…

We perform a numerical study on the application of electromagnetic flux on a heterogeneous network of Chialvo neurons represented by a ring-star topology. Heterogeneities are realized by introducing additive noise modulations on both the…

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…

The study of chimera states or, more generally, coherence-incoherence patterns has led to the development of several tools for their identification and characterization. In this work, we extend the eigenvalue decomposition method to…

In this paper, we study random dynamical systems generated by two Allee maps. Two models are considered - with and without small random perturbations. It is shown that the behavior of the systems is very similar to the behavior of the…