相关论文: Periodic travelling waves in the theta model for s…

We study rotating waves in the Theta model for a ring of synaptically-interacting neurons. We prove that when the neurons are oscillatory, at least one rotating wave always exists. In the case of excitable neurons, we prove that no…

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…

The present paper is concerned with the existence of traveling wave solutions of the asymptotic model, derived by the authors in a previous work, to approximate the unidirectional evolution of a collision-free plasma in a magnetic field.…

We study the propagation of an unusual type of periodic travelling waves in chains of identical beads interacting via Hertz's contact forces. Each bead periodically undergoes a compression phase followed by a free flight, due to special…

In this paper, we investigate the existence, uniqueness, and spectral stability of traveling waves arising from a single threshold neural field model with one spatial dimension, a Heaviside firing rate function, axonal propagation delay,…

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…

We consider a pair of identical theta neurons in the excitable regime, each coupled to the other via a delayed Dirac delta function with the same delay. This simple network can support different periodic solutions, and we concentrate on two…

The purpose of this work is to introduce a concept of traveling waves in the setting of periodic metric graphs. It is known that the nonlinear Schr{\"o}dinger (NLS) equation on periodic metric graphs can be reduced asymptotically on long…

We study wave propagation in networks of coupled cells which can behave as excitable or self-oscillatory media. For excitable media, an asymptotic construction of wave trains is presented. This construction predicts their shape and speed,…

In the dynamics generated by the suspension bridge equation, traveling waves are an essential feature. The existing literature focuses primarily on the idealized one-dimensional case, while traveling structures in two spatial dimensions…

We prove a principle of linearized stability for traveling wave solutions to neural field equations posed on the real line. Additionally, we provide the existence of a finite dimensional invariant center manifold close to a traveling wave,…

Spatiotemporal patterns such as traveling waves are frequently observed in recordings of neural activity. The mechanisms underlying the generation of such patterns are largely unknown. Previous studies have investigated the existence and…

The existence of travelling waves for a model of concentration waves of bacteria is investigated. The model consists in a kinetic equation for the biased motion of cells following a run-and-tumble process, coupled with two…

We consider a lattice equation modelling one-dimensional metamaterials formed by a discrete array of nonlinear resonators. We focus on periodic travelling waves due to the presence of a periodic force. The existence and uniqueness results…

In Rapela (2016) we reported traveling waves (TWs) on electrocorticographic (ECoG) recordings from an epileptic subject over speech processing brain regions, while the subject rhythmically produced consonant-vowel syllables (CVSs). In…

Traveling waves of neural activity emerge in cortical networks both spontaneously and in response to stimuli. The spatiotemporal structure of waves can indicate the information they encode and the physiological processes that sustain them.…

Travelling waves of neural firing activity are observed in brain tissue as a part of various sensory, motor and cognitive processes. They represent an object of major interest in the study of excitable networks, with analysis conducted in…

We prove the existence and uniqueness, for wave speeds sufficiently large, of monotone traveling wave solutions connecting stable to unstable spatial equilibria for a class of $N$-dimensional lattice differential equations with…

Natural and technological networks exhibit dynamics that can lead to complex cooperative behaviors, such as synchronization in coupled oscillators and rhythmic activity in neuronal networks. Understanding these collective dynamics is…

Motivated by earlier studies of artificial perceptions of light called phosphenes, we analyze traveling wave solutions in a chain of periodically forced coupled nonlinear oscillators modeling this phenomenon. We examine the discrete model…