Generic dynamical systems are characterized by the coexistence of chaotic regions and regular structures, and typical trajectories present regular segments, due to sticking to the ordered component of the phase space, separated by erratic behavior, due to wanderings in the chaotic sea. Though ubiquitous, this mixed behavior still involves hard theoretical problems, as present theories are tailo...

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...

Estimating parameters of a model system using observed chaotic scalar time series data is a topic of active interest. To estimate these parameters requires a suitable similarity indicator between the observed and model systems. Many works have considered a similarity measure in the time domain, which has limitations because of sensitive dependence on initial conditions. On the other hand, there...

This research deals with a utilization of a tool for symbolic regression, which is analytic programming, for the purpose of the synthesis of a new robust control law. This universal synthesized robust chaotic controller secures the fully stabilization of selected set of discrete chaotic systems. The paper consists of the descriptions of analytic programming as well as selected chaotic systems, ...

This research deals with a utilization of tool for symbolic regression, which is analytic programming, for the purpose of the synthesis of a new control law. This synthesized chaotic controller secures the stabilization of high periodic orbit – oscillations between several values of discrete chaotic system, which is Hénon map. The paper consists of the descriptions of analytic programming as we...

Grebogi, Ott and Yorke (Phys. Rev. A 38(7), 1988) have investigated the effect of finite precision on average period length of chaotic maps. They showed that the average length of periodic orbits (T ) of a dynamical system scales as a function of computer precision (ε) and the correlation dimension (d) of the chaotic attractor: T ∼ ε. In this work, we are concerned with increasing the average p...

We study the occurence of delay mechanisms other than periodic orbits in systems with time dependent potentials that exhibit chaotic scattering. By using as model system two harmonically oscillating disks on a plane, we have found the existence of a mechanism not related to the periodic orbits of the system, that delays trajectories in the scattering region. This mechanism creates a fractal-lik...

Chaotic iterations, a tool formerly used in distributed computing, has recently revealed various interesting properties of disorder leading to its use in the computer science security field. In this paper, a comprehensive study of its topological behavior is proposed. It is stated that, in addition to being chaotic as defined in the Devaney’s formulation, this tool possesses the property of top...

This paper proposes a new sliding mode control (SMC)  based model reference adaptive system (MRAS) for sensorless indirect field oriented control (IFOC) of a single-sided linear induction motor (SLIM). The operation of MRAS speed estimators dramatically depends on adaptation mechanism. Fixed-gain PI controller is conventionally used for this purpose which may fail to estimate the speed correctl...

To overcome the complexities in Type-2 Fuzzy Sets (T2FSs) and to present a general model for chaotic FSs, this paper introduces new FSs called Bifurcating FSs (BFSs). The BFS is inspired from human brain. Mathematically, it is equivalent to the coupled chaotic map in which one of the variables is a fuzzy membership function. Biologically, it is equivalent to the oscillatory neuron in which a fu...