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An ensemble of pulse-coupled phase-oscillators is thoroughly analysed in the presence of a mean-field coupling and a dispersion of their natural frequencies. In spite of the analogies with the Kuramoto setup, a much richer scenario is…
The present work studies the influence of nonlocal spatial coupling on the existence of localized structures in 1-dimensional extended systems. We consider systems described by a real field with a nonlocal coupling that has a linear…
A common model to study pattern formation in large groups of neurons is the neural field. We investigate a neural field with excitatory and inhibitory neurons, like Wilson and Cowan (1972), with transmission delays and gap junctions. We…
In this work, we study the dynamics of a spatially heterogeneous single population model with the memory effect and nonlinear boundary condition. By virtue of the implicit function theorem and Lyapunov-Schmidt reduction, spatially…
The analysis on stability and bifurcations in the macroscopic dynamics exhibited by the system of two coupled large populations comprised of $N$ stochastic excitable units each is performed by studying an approximate system, obtained by…
From cytoskeletal networks to tissues, many biological systems behave as active materials. Their composition and stress-generation is affected by chemical reaction networks. In such systems, the coupling between mechanics and chemistry…
We consider the effect of distributed delays in neural feedback systems. The avian optic tectum is reciprocally connected with the nucleus isthmi. Extracellular stimulation combined with intracellular recordings reveal a range of signal…
In a first step towards the comprehension of neural activity, one should focus on the stability of the various dynamical states. Even the characterization of idealized regimes, such as a perfectly periodic spiking activity, reveals…
Real-world dynamical systems with retardation effects are described in general not by a single, precisely defined time delay, but by a range of delay times. An exact mapping onto a set of $N+1$ ordinary differential equations exists when…
We present a detailed study of a scalar differential equation with threshold state-dependent delayed feedback. This equation arises as a simplification of a gene regulatory model. There are two monotone nonlinearities in the model: one…
We study the emergence of symmetric oscillatory behavior in multi-agent systems where each agent incorporates a continuous memory of its past states and past rates of change, modeled by distributed retarded and neutral delays. The…
Despite substantial progress in deep learning approaches to time-series reconstruction, no existing methods are designed to uncover local activities with minute signal strength due to their negligible contribution to the optimization loss.…
Neural circuits exhibit remarkable computational flexibility, enabling adaptive responses to noisy and ever-changing environmental cues. A fundamental question in neuroscience concerns how a wide range of behaviors can emerge from a…
Long-range speckle correlations play an essential role in wave transport through disordered media, but have rarely been studied in other complex systems. Here we discover spatio-temporal intensity correlations for an optical pulse…
We study numerically the effects of time delay in networks of delay-coupled excitable FitzHugh Nagumo systems with dissipation. The generation of periodic self-sustained oscillations and its threshold are analyzed depending on the…
Flexible modulation of temporal dynamics in neural sequences underlies many cognitive processes. For instance, we can adaptively change the speed of motor sequences and speech. While such flexibility is influenced by various factors such as…
Localized patterns in singularly perturbed reaction-diffusion equations typically consist of slow parts -- in which the associated solution follows an orbit on a slow manifold in a reduced spatial dynamical system -- alternated by fast…
We study the emergence and the stability of temporal localized structures in the output of a semiconductor laser passively mode-locked by a saturable absorber in the long cavity regime. For large yet realistic values of the linewidth…
We study synaptically coupled neuronal networks to identify the role of coupling delays in network's synchronized behaviors. We consider a network of excitable, relaxation oscillator neurons where two distinct populations, one excitatory…
We propose a paradigmatic model system, a subcritical Hopf normal form subjected to noise and time-delayed feedback, to investigate the impact of time delay on coherence resonance in non-excitable systems. We develop analytical tools to…