A novel concept for controlling of nonlinear systems using chaos and fuzzy model-based regulators is presented. In the control of such systems, we employ two phases, the first of which uses open-loop control forming a chaotic attractor or using chaotic inherent features in a system itself. Once the system states reach a predefined convex domain, open-loop control is cut off and a fuzzy model-ba...

All nondegenerate, continuous, piecewise-linear maps on [Formula: see text] with two pieces are equivalent to a member of four-parameter family known as the two-dimensional border-collision normal form. This paper shows how powerful technique renormalization can be applied this and reveals previously undescribed bifurcation structure in succinct way. We partition parameter region where is exhib...

The article presents the results of the study of nonlinear market prices dynamic, simulated using game theory model, maps and theory of bifurcation. Market pricing is presented as a two-dimensional map. Qualitative analyses of the firms’ pricing system properties using the fixed points, analysis of the trajectories near these fixed points were fulfilled Simulation of the market prices dynamic s...

Chaotic scattering in open Hamiltonian systems is relevant for different problems in physics. Particles in such kind of systems can exhibit both bounded or unbounded motions for which escapes from the scattering region can take place. This paper analyzes how to control the escape of the particles from the scattering region in the presence of noise. For that purpose, we apply the partial control...

The present paper is aimed at introducing a new algorithm for image encryption using chaotic tent maps and the desired key image. This algorithm consists of two parts, the first of which works in the frequency domain and the second, in the time domain. In the frequency domain, a desired key image is used, and a random number is generated, using the chaotic tent map, in order to change the phase...

This paper proposes the optimal control methods for a class of chaotic systems via state feedback. By converting the chaotic systems to the form of uncertain piecewise linear systems, we can obtain the optimal controller minimizing the upper bound on cost function by virtue of the robust optimal control method of piecewise linear systems, which is cast as an optimization problem under constrain...

Background: Photon attenuation as an inevitable physical phenomenon influences on the diagnostic information of SPECT images and results to errors in accuracy of quantitative measurements. This can be corrected via different physical or mathematical approaches. As the correction equation in mathematical approaches is nonlinear, in this study a new method of linearization called ‘Piece ...

We study the synchronization of a linear array of globally coupled identical logistic maps. We consider a time-delayed coupling that takes into account the finite velocity of propagation of the interactions. We find globally synchronized states in which the elements of the array evolve along a periodic orbit of the uncoupled map, while the spatial correlation along the array is such that an ind...

The knowledge of transitions between regular, laminar or chaotic behaviors is essential to understand the underlying mechanisms behind complex systems. While several linear approaches are often insufficient to describe such processes, there are several nonlinear methods that, however, require rather long time observations. To overcome these difficulties, we propose measures of complexity based ...

B-spline neural network (BSNN), a type of basis function neural network, is trained by gradient-based methods, which may fall into local minimum during the learning procedure. To overcome the problems encountered by the conventional learning methods, differential evolution (DE)  an evolutionary computation methodology  can provide a stochastic search to adjust the control points of a BSNN are...