Related papers: Pattern Formation in Excitable Neuronal Maps
In the first half of the paper, some recent advances in coupled dynamical systems, in particular, a globally coupled map are surveyed. First, dominance of Milnor attractors in partially ordered phase is demonstrated. Second, chaotic…
In this work, we construct a novel two-dimensional discrete neuron map by incorporating a cosine-based memristor into the reduced Chialvo neuron map to examine the dynamical analysis of electromagnetic modulation. The nonlinear…
We study the non-equilibrium pattern formation that emerges when magnetically repelling colloids, trapped by optical tweezers, are abruptly released, forming colloidal explosions. For multiple colloids in a single trap we observe a pattern…
Spiral waves are self-repeating waves that can form in excitable media, propagating outward from their center in a spiral pattern. Spiral waves have been observed in different natural phenomena and have been linked to medical conditions…
Neurons are often connected, spatially and temporally, in phenomenal ways that promote wave propagation. Therefore, it is essential to analyze the emergent spatiotemporal patterns to understand the working mechanism of brain activity,…
A central question in neuroscience is to understand how noisy firing patterns are used to transmit information. Because neural spiking is noisy, spiking patterns are often quantified via pairwise correlations, or the probability that two…
(Bi)multi-partite interaction patterns are commonly observed in real world systems which have inhibitory and excitatory couplings. We hypothesize these structural interaction pattern to be stable and naturally arising in the course of…
Excitable media are systems which are at rest in the absence of external input but which respond to a sufficiently strong stimulus by sending a wave of "excitation" across the medium. Examples include cardiac and cortical tissue, and in…
A simple model that replicates the dynamics of spiking and spiking-bursting activity of real biological neurons is proposed. The model is a two-dimensional map which contains one fast and one slow variable. The mechanisms behind generation…
We study a driven-dissipative duo of two-level systems in an open quantum systems approach, modelling a pair of atoms or (more generally) meta-atoms. Allowing for complex-valued couplings in the setup, which are of both a coherent and…
Fully developed turbulence is a universal and scale-invariant chaotic state characterized by an energy cascade from large to small scales where the cascade is eventually arrested by dissipation. In this article, we show how to harness these…
This review gives a short historical account of the excitable maps approach for modeling neurons and neuronal networks. Some early models, due to Pasemann (1993), Chialvo (1995) and Kinouchi and Tragtenberg (1996), are compared with more…
Oscillatory dynamics of complex networks has recently attracted great attention. In this paper we study pattern formation in oscillatory complex networks consisting of excitable nodes. We find that there exist a few center nodes and small…
Spiking neural network models characterize the emergent collective dynamics of circuits of biological neurons and help engineer neuro-inspired solutions across fields. Most dynamical systems' models of spiking neural networks typically…
Describing the collective activity of neural populations is a daunting task: the number of possible patterns grows exponentially with the number of cells, resulting in practically unlimited complexity. Recent empirical studies, however,…
Takens constructed a residual subset of the state space consisting of initial points with historic behaviour for expanding maps on the circle. We prove that this statistical property of expanding maps on the circle is preserved under small…
We consider the dynamical effects of electromagnetic flux on the discrete Chialvo neuron. It is shown that the model can exhibit rich dynamical behaviors such as multistability, firing patterns, antimonotonicity, closed invariant curves,…
We examine traveling-wave solutions on a regular ring network with one additional long-range link that spans a distance d. The nodes obey the FitzHugh-Nagumo kinetics in the excitable regime. The additional shortcut induces a plethora of…
We investigate the spatiotemporal dynamics of coupled circle map lattices, evolving under synchronous (parallel) updating on one hand and asynchronous (random) updating rules on the other. Synchronous evolution of extended spatiotemporal…
We study random circle maps that are expanding on the average. Uniform bounds on neither expansion nor distortion are required. We construct a coupling scheme, which leads to exponential convergence of measures (memory loss) and exponential…