相关论文: Chaos in neural networks with a nonmonotonic trans…
Chaotic functions are characterized by sensitivity to initial conditions, transitivity, and regularity. Providing new functions with such properties is a real challenge. This work shows that one can associate with any Boolean network a…
A multidimensional chaos is generated by a special initial value problem for the non-autonomous impulsive differential equation. The existence of a chaotic attractor is shown, where density of periodic solutions, sensitivity of solutions…
Chaos is an inherently dynamical phenomenon traditionally studied for trajectories that are either permanently erratic or transiently influenced by permanently erratic ones lying on a set of measure zero. The latter gives rise to the final…
We study a deterministic dynamics with two time scales in a continuous state attractor network. To the usual (fast) relaxation dynamics towards point attractors (``patterns'') we add a slow coupling dynamics that makes the visited patterns…
Anatomical studies demonstrate that brain reformats input information to generate reliable responses for performing computations. However, it remains unclear how neural circuits encode complex spatio-temporal patterns. We show that neural…
Characterizing the emergence of chaotic dynamics of complex networks is an essential task in nonlinear science with potential important applications in many fields such as neural control engineering, microgrid technologies, and ecological…
A walker is the association of a sub-millimetric bouncing drop moving along with a co-evolving Faraday wave. When confined in a harmonic potential, its stable trajectories are periodic and quantised both in extension and mean angular…
Biological information processing is often carried out by complex networks of interconnected dynamical units. A basic question about such networks is that of reliability: if the same signal is presented many times with the network in…
An attractor of a piecewise-smooth continuous system of differential equations can bifurcate from a stable equilibrium to a more complicated invariant set when it collides with a switching manifold under parameter variation. Here numerical…
Further analysis and experimentation is carried out in this paper for a chaotic dynamic model, viz. the Nonlinear Dynamic State neuron (NDS). The analysis and experimentations are performed to further understand the underlying dynamics of…
We study the effect of various transfer functions on the properties of a time series generated by a continuous-valued feed-forward network in which the next input vector is determined from past output values. The parameter space for…
The striking fractal geometry of strange attractors underscores the generative nature of chaos: like probability distributions, chaotic systems can be repeatedly measured to produce arbitrarily-detailed information about the underlying…
Spatio-temporal network dynamics is an emergent property of many complex systems which remains poorly understood. We suggest a new approach to its study based on the analysis of dynamical motifs -- small subnetworks with periodic and…
The dynamics on a chaotic attractor can be quite heterogeneous, being much more unstable in some regions than others. Some regions of a chaotic attractor can be expanding in more dimensions than other regions. Imagine a situation where two…
We present a neurobiologically--inspired stochastic cellular automaton whose state jumps with time between the attractors corresponding to a series of stored patterns. The jumping varies from regular to chaotic as the model parameters are…
Continuous-time systems with switch-like behaviour occur in chemical kinetics, gene regulatory networks and neural networks. Networks with hard switching, as a limiting case of smooth sigmoidal switching, retain the richest possible range…
As a phenomenon in dynamical systems allowing autonomous switching between stable behaviors, chaotic itinerancy has gained interest in neurorobotics research. In this study, we draw a connection between this phenomenon and the predictive…
The properties of time series generated by a perceptron with monotonic and non-monotonic transfer function, where the next input vector is determined from past output values, are examined. Analysis of the parameter space reveals the…
One of the common characteristics of chaotic maps or flows in high dimensions is "unstable dimensional variability", in which there are periodic points whose unstable manifolds have different dimensions. In this paper, in trying to…
Effect of noise in inducing order on various chaotically evolving systems is reviewed, with special emphasis on systems consisting of coupled chaotic elements. In many situations it is observed that the uncoupled elements when driven by…