This paper discusses the analysis and computations of chaos–hyperchaos (or vice versa) transition in Rössler–Nikolov–Clodong O (RNC-O) hyperchaotic system. Our work is motivated by our previous transitional regimes RNC-O system results recently obtained from another researchers. The numerical simulations show that coupled to change equilibria type as one large attractor occurs. Moreover, we for...

We consider Berry's random planar wave model (1977), and prove spatial functional limit theorems - in the high-energy for discretized truncated versions of field obtained by restricting its nodal length to rectangular domains. Our analysis is crucially based on a detailed study projection lengths onto so-called second Wiener chaos, whose fluctuations are given Gaussian total disorder indexed po...

An exact low-dimensional system of mean-field equations for an infinite-size network pulse coupled integrate-and-fire neurons with a bimodal distribution excitability parameter is derived. Bifurcation analysis these shows rich variety dynamic modes that do not exist unimodal this parameter. New include multistable equilibrium states different levels the spiking rate, collective oscillations and...

Abstract In this paper, an implicit nonsymplectic exact energy-preserving integrator is specifically designed for a ten-dimensional phase-space conservative Hamiltonian system with five degrees of freedom. It based on suitable discretization-averaging the gradient, second-order accuracy to numerical solutions. A one-dimensional disordered discrete nonlinear Schrödinger equation and post-Newtoni...

We investigate toy dynamical models of energy-level repulsion in quantum eigenvalue sequences. We focus on parametric (with respect to a running coupling or ”complexity” parameter) stochastic processes that are capable of relaxing towards a stationary regime (e. g. equilibrium, invariant asymptotic measure). In view of ergodic property, that makes them appropriate for the study of short-range f...

Chaotic dynamics can be effectively studied by continuation from an anti-integrable limit. Using the Hénon map as an example, we obtain a simple analytical bound on the domain of existence of the horseshoe that is equivalent to the well-known bound of Devaney and Nitecki. We also reformulate the popular method for finding periodic orbits introduced by Biham and Wenzel. Near an anti-integrable l...

Road traffic volumes in intercity roads are generally estimated by probability functions, statistical techniques or meta-heuristic approaches such as artificial neural networks. As the road traffic volumes depend on input variables and mainly road geometrical design, weather conditions, day or night time, weekend or national holidays and so on, these are also estimated by pattern recognition te...