Related papers: Stable chaos
The concept of deterministic dynamical chaos has a long history and is well established by now. Nevertheless, its field theoretic essence and its stochastic generalization have been revealed only very recently. Within the newly found…
Chaotic cryptography describes the use of chaos theory (in particular physical dynamical systems working in chaotic regime as part of communication techniques and computation algorithms) to perform different cryptographic tasks in a…
The dynamics of a disordered nonlinear chain can be either regular or chaotic with a certain probability. The chaotic behavior is often associated with the destruction of Anderson localization by the nonlinearity. In the presentwork it is…
Highly connected recurrent neural networks often produce chaotic dynamics, meaning their precise activity is sensitive to small perturbations. What are the consequences for how such networks encode streams of temporal stimuli? On the one…
In this set of lectures, we review briefly some of the recent developments in the study of the chaotic dynamics of nonlinear oscillators, particularly of damped and driven type. By taking a representative set of examples such as the…
The phenomenon of Stochastic Resonance (SR) is reported in a completely noise-free situation, with the role of thermal noise being taken by low-dimensional chaos. A one-dimensional, piecewise linear map and a pair of coupled…
We show that the existence of a dense set of periodic points for a topologically transitive non-minimal continuous group action on a Hausdorff uniform space with an infinite acting group does not necessarily imply a sensitive dependence to…
Dynamics in biological networks are in general robust against several perturbations. We investigate a coupled map network as a model motivated by gene regulatory networks and design systems which are robust against phenotypic perturbations…
Phase-coupled oscillators serve as paradigmatic models of networks of weakly interacting oscillatory units in physics and biology. The order parameter which quantifies synchronization was so far found to be chaotic only in systems with…
Chaos presents complex dynamics arising from nonlinearity and a sensitivity to initial states. These characteristics suggest a depth of expressivity that underscores their potential for advanced computational applications. However,…
A collective chaotic phase with power law scaling of activity events is observed in a disordered mean field network of purely excitatory leaky integrate-and-fire neurons with short-term synaptic plasticity. The dynamical phase diagram…
A nonuniform system is considered consisting of two phases with different densities of particles. At each given time the distribution of the phases in space is chaotic: each phase filling a set of regions with random shapes and locations. A…
We propose a neural network model with transient chaos, or a transiently chaotic neural network (TCNN) as an approximation method for combinatorial optimization problem, by introducing transiently chaotic dynamics into neural networks.…
This paper deals with classes of (de)stabilizing switching signals for switched systems. Most of the available conditions for stability of switched systems are sufficient in nature, and consequently, their violation does not conclude…
The problem of Turing pattern formation has attracted much attention in nonlinear science as well as physics, chemistry and biology. So far all Turing patterns have been observed in stationary and oscillatory media only. In this letter we…
We study the time-evolution of cumulants of velocities and kinetic energies in the stochastic Kac model for velocity exchange of $N$ particles, with the aim of quantifying how fast these degrees of freedom become chaotic in a time scale in…
We study statistical properties of the irregular bursting arising in a class of neuronal models close to the transition from spiking to bursting. Prior to the transition to bursting, the systems in this class develop chaotic attractors,…
While classical chaos is defined via a system's sensitive dependence on its initial conditions (SDIC), this notion does not directly extend to quantum systems. Instead, recent works have established defining both quantum and classical chaos…
We give a definition of chaos for a continuous self-map of a general topological space. This definition coincides with the Devanney definition for chaos when the topological space happens to be a metric space. We show that in a uniform…
The goal of polyhomeostatic control is to achieve a certain target distribution of behaviors, in contrast to polyhomeostatic regulation which aims at stabilizing a steady-state dynamical state. We consider polyhomeostasis for individual and…