Abstract This paper discusses a novel “chaotic” form of superbanana transport, and compares theory to experiments on nonneutral plasmas. Superbanana transport is caused by particles that cross local trapping separatrices (magnetic or electric ripples) in the presence of field “errors” such as toroidal magnetic curvature. Traditionally, collisions (at rate ν) cause separatrix crossings, with res...

The chaotic behavior of the Rabinovich–Fabrikant system, a model with multiple topologically different chaotic attractors, is analyzed. Because of the complexity of this system, analytical and numerical studies of the system are very difficult tasks. Following the investigation of this system carried out in [Danca & Chen, 2004], this paper verifies the presence of multiple chaotic attractors in...

In this paper, we study chaotic synchronization in 1D lattices of two-variable maps coupled with one variable. We give a rigourous proof for the occurrence of chaotic synchronization of spatially homogeneous solutions in such coupled map lattices (CMLs) of lattice size n = 4 with suitable coupling coefficients. For the case of lattice size n > 4, we demonstrate numerical results of synchronized...

Chaotic strings are particular classes of coupled map lattices that can serve as models for vacuum fluctuations in stochastically quantized field theories. They have been previously shown to distinguish standard model coupling parameters as corresponding to states of strongest possible chaotic behaviour and vanishing nearest-neighbour correlation. In this paper we look at discrete symmetry tran...

We study a plethora of chaotic phenomena in the Hindmarsh-Rose neuron model with the use of several computational techniques including the bifurcation parameter continuation, spike-quantification, and evaluation of Lyapunov exponents in bi-parameter diagrams. Such an aggregated approach allows for detecting regions of simple and chaotic dynamics, and demarcating borderlines-exact bifurcation cu...

In this report, we investigate phenomena on the edge of spatially uniform chaotic mode and spatial temporal chaos in a lattice of chaotic 1-D maps with only local connections. It is shown that in autonomous lattice with local connections, spatially uniform chaotic mode cannot exist if the Lyapunov exponent λ of the isolated chaotic map is greater than some critical value λcr > 0. We proposed a ...

The relationship between chaos and cryptography makes it natural to employ chaotic systems to design new cryptosystems. It is based on the facts that chaotic signals are usually noise-like and chaotic systems are very sensitive to initial conditions. Their sensitivity to initial conditions and their spreading out of trajectories over the whole interval seems to be a model that satisfies the cla...

The minimum vertex cover (MVC) problem is a classic graph optimization problem. It is well known that it is an NP-Complete problem. By analyzing the dynamic behavior of the transiently chaotic neural network and the characteristics of the minimum vertex cover problem, we propose a specialized transiently chaotic neural network for this problem. Extensive simulation results show that the transie...

In order to exploit generalized chaotic synchronization phenomena for the solution of temporal pattern recognition problems, a chaotic dynamical system representing the class of signals that are to be recognized must be established. This system can be determined by means of identification techniques. Although the fulfillment of the chaotic condition could appear as a constraint, it is shown her...

The non-linear dynamics of the chaotic 1D logistic map and its statistical and spectral properties are studied using MATLAB numerical simulations. We have developed an analog behavioral model and implemented logistic map on a field programmable analog array chip. Presented measurement results confirmed the chaotic behavior of the implemented system. Results show that field programmable analog a...