Related papers: Final state sensitivity and fractal basin boundari…
We analyze the dynamics of two coupled identical populations of quadratic integrate-and-fire neurons, which represent the canonical model for class I neurons near the spiking threshold. The populations are heterogeneous; they include both…
Power grids sustain modern society by supplying electricity and thus their stability is a crucial factor for our civilization. The dynamic stability of a power grid is usually quantified by the probability of its nodes' recovery to phase…
A discussion about dependences of the (fractal) basin boundary dimension with the definition of the basins and the size of the exits is presented for systems with one or more exits. In particular, it is shown that the dimension is largely…
We continue the study of a stochastic system of interacting neurons introduced in De Masi-Galves-L\"ocherbach-Presutti (2014). The system consists of N neurons, each spiking randomly with rate depending on its membrane potential. At its…
Noise play a creative role in the evolution of periodic and complex systems which are essential for continuous performance of the system. The interaction of noise generated within one component of a chaotic system with other component in a…
This paper presents an investigation of the dynamics of two coupled non-identical FitzHugh-Nagumo neurons with quadratic term and delayed synaptic connection. We consider coupling strength and time delay as bifurcation parameters, and try…
Real-world systems often evolve on different timescales and possess multiple coexisting stable states. Whether or not a system returns to a given stable state after being perturbed away from it depends on the shape and extent of its basin…
Low-dimensional yet rich dynamics often emerge in the brain. Examples include oscillations and chaotic dynamics during sleep, epilepsy, and voluntary movement. However, a general mechanism for the emergence of low dimensional dynamics…
The ${\bf E}\times{\bf B}$ drift motion of particles in tokamaks provides valuable information on the turbulence-driven anomalous transport. One of the characteristic features of the drift motion dynamics is the presence of chaotic orbits…
We present a perception model of ambiguous patterns based on the chaotic neural network and investigate the characteristics through computer simulations. The results induced by the chaotic activity are similar to those of psychophysical…
The deterministic dynamics of randomly connected neural networks are studied, where a state of binary neurons evolves according to a discreet-time synchronous update rule. We give a theoretical support that the overlap of systems' states…
Extreme multistability (EM) is characterized by the emergence of infinitely many coexisting attractors or continuous families of stable states in dynamical systems. EM implies complex and hardly predictable asymptotic dynamical behavior. We…
Time evolution of diluted neural networks with a nonmonotonic transfer function is analitically described by flow equations for macroscopic variables. The macroscopic dynamics shows a rich variety of behaviours: fixed-point, periodicity and…
We study synchronization of non-diffusively coupled map networks with arbitrary network topologies, where the connections between different units are, in general, not symmetric and can carry both positive and negative weights. We show that,…
Spontaneous brain activity in the absence of external stimuli is not random but contains complex dynamical structures such as neuronal avalanches with power-law duration and size distributions. These experimental observations have been…
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…
While most models of randomly connected networks assume nodes with simple dynamics, nodes in realistic highly connected networks, such as neurons in the brain, exhibit intrinsic dynamics over multiple timescales. We analyze how the…
We study quantum-mechanical tunneling in mixed dynamical systems between symmetry-related phase space tori separated by a chaotic layer. Considering e.g. the annular billiard we decompose tunneling-related energy splittings and shifts into…
The stability of synchronous states is analysed in the context of two populations of inhibitory and excitatory neurons, characterized by different pulse-widths. The problem is reduced to that of determining the eigenvalues of a suitable…
We theoretically investigate the flow of the atomic excitations in a driven chiral-coupled atomic chain with nonreciprocal decay channels. This one-dimensional system allows infinite-range dipole-dipole interaction, and enables directional…