Related papers: Dynamical Phase Transitions In Driven Integrate-An…

We propose a dynamical mechanism of the two-way switching between the metastable state and the stable state, which has been found in experiments of photoinduced reversible magnetization and photoinduced structural phase transition. We find…

In this paper, we investigate the fundamental limits on how the inter- spike time of a neuron oscillator can be perturbed by the application of a bounded external control input (a current stimulus) with zero net electric charge…

The cooperative behavior of neurons and neuronal areas associated with the synchronization behavior proves to be a fundamental neural mechanism. In addition, abnormal levels of synchronization have been related to unhealthy neural…

Elucidating the neurophysiological mechanisms underlying neural pattern formation remains an outstanding challenge in Computational Neuroscience. In this paper, we address the issue of understanding the emergence of neural patterns by…

We consider a heterogeneous, globally coupled population of excitatory quadratic integrate-and-fire neurons with excitability adaptation due to a metabolic feedback associated with ketogenic diet, a form of therapy for epilepsy. Bifurcation…

The properties of a front between two different phases in the presence of a smoothly inhomogeneous external field that takes its critical value at the crossing point is analyzed. Two generic scenarios are studied. In the first, the system…

Neurons in the brain behave as a network of coupled nonlinear oscillators processing information by rhythmic activity and interaction. Several technological approaches have been proposed that might enable mimicking the complex information…

We consider the dynamical properties of a simple model of vibrational surface modes. We obtain the exact spectrum of surface excitations and discuss their dynamical features. In addition to the usually discussed localized and oscillatory…

This paper presents a stability analysis of simple neuromodules displaying fold bifurcations (leading to hysteresis), flip bifurcations (period doubling and undoubling to and from chaos) and Neimark-Sacker bifurcations (quasiperiodic and…

This study investigates the existence and stability of limit cycles resulting from self-excited oscillations in linear multi-degree-of-freedom systems subjected to discontinuous, state-dependent forcing. Using the method of averaging and…

Brain rhythms contribute to every aspect of brain function. Here, we study critical and resonance phenomena that precede the emergence of brain rhythms. Using an analytical approach and simulations of a cortical circuit model of neural…

The paper examines the discrete-time dynamics of neuron models (of excitatory and inhibitory types) with piecewise linear activation functions, which are connected in a network. The properties of a pair of neurons (one excitatory and the…

We present a detailed analysis of the dynamical regimes observed in a balanced network of identical Quadratic Integrate-and-Fire (QIF) neurons with a sparse connectivity for homogeneous and heterogeneous in-degree distribution. Depending on…

Understanding how deep neural networks learn remains a fundamental challenge in modern machine learning. A growing body of evidence suggests that training dynamics undergo a distinct phase transition, yet our understanding of this…

We study in this paper the effect of an unique initial stimulation on random recurrent networks of leaky integrate and fire neurons. Indeed given a stochastic connectivity this so-called spontaneous mode exhibits various non trivial…

Phase resetting is a common experimental approach to investigating the behaviour of oscillating neurons. Assuming repeated spiking or bursting, a phase reset amounts to a brief perturbation that causes a shift in the phase of this periodic…

Conventional digital computation is rapidly approaching physical limits for speed and energy dissipation. Here we fabricate and test a simple neuromorphic circuit that models neuronal somas, axons and synapses with superconducting Josephson…

In this paper, we consider the nonlinear dynamical behaviors of some tabu leaning neuron models. We first consider a tabu learning single neuron model. By choosing the memory decay rate as a bifurcation parameter, we prove that Hopf…

In dynamical systems on networks, one assigns the dynamics to nodes, which are then coupled via links. This approach does not account for group interactions and dynamics on links and other higher dimensional structures. Higher-order network…

We consider a two-dimensional fully frustrated Josephson-junction array, which is driven uniformly by oscillating currents. As the temperature is lowered, there emerges a dynamic phase transition to an ordered state with nonzero dynamic…