Tomasz Kapitaniak

HYPERCHAOTIC ATTRACTORS OF UNIDIRECTIONALLY-COUPLED CHUA’S CIRCUITS

In this letter we discuss properties of hyperchaotic attractors of unidirectionally-coupled Chua’s circuits. Results from chaos synchronization theory allowed us to observe chaos-hyperchaos transition on 3D projections of the attractor.

Experimental hyperchaos in coupled Chua's circuits

In this letter we report experimental observation of hyperchaotic attractors in open and closed chains of Chuas circuits. >

Kelvin-Voigt versus Bürgers internal damping in modeling of axially moving viscoelastic web

Stability and oscillation characteristics of two-dimensional axially moving web have been investigated. The application of one-dimensional beam-like models of the web allows the identi1cation of instability regions and the estimation of the critical speed. For the beam material two di3erent models, i.e., Kelvin–Voigt and B # have been considered. The numerical solutions of full non-linear and linearized equations have been compared. The e3ects of axially travelling speed and the internal damping on dynamical stability of axially moving web have been studied in details. Our numerical studies of Kelvin– Voigt and Burger’s models show that both models give similar results for small values of internal damping and can be used to describe the dynamics of axially moving webs made from materials with internal damping coe7cient smaller than 3 × 10 −5 . For the materials with larger damping coe7cient the B # urgers model gives more reliable results. ? 2002 Elsevier

Hysteretic effects of dry friction: modelling and experimental studies.

In this paper, the phenomena of hysteretic behaviour of friction force observed during experiments are discussed. On the basis of experimental and theoretical analyses, we argue that such behaviour can be considered as a representation of the system dynamics. According to this approach, a classification of friction models, with respect to their sensitivity on the system motion characteristic, is introduced. General friction modelling of the phenomena accompanying dry friction and a simple yet effective approach to capture the hysteretic effect are proposed. Finally, the experimental results are compared with the numerical simulations for the proposed friction model.

Continuous Control and Synchronization in Chaotic Systems

We show that two identical chaotic systems can be synchronized by applying the method of continuous chaos control. The developed method is especially useful for higher-dimensional systems. We also discuss the possible applications of our synchronization scheme in geophysical systems.

Co-existing attractors of impact oscillator

Abstract Co-existing attractors of a mechanical system with impacts and dry friction are discussed in this paper. Our investigations have shown that, in the systems with noise, not all attractors can be reached by system trajectories.

MONOTONE SYNCHRONIZATION OF CHAOS

In this letter we show that the monotone synchronization is possible for chaotic systems and can be easily obtained using the method of continuous chaos control. We also discuss possible applications of this type of synchronization for secure communications.

Imperfect chimera states for coupled pendula.

The phenomenon of chimera states in the systems of coupled, identical oscillators has attracted a great deal of recent theoretical and experimental interest. In such a state, different groups of oscillators can exhibit coexisting synchronous and incoherent behaviors despite homogeneous coupling. Here, considering the coupled pendula, we find another pattern, the so-called imperfect chimera state, which is characterized by a certain number of oscillators which escape from the synchronized chimeras cluster or behave differently than most of uncorrelated pendula. The escaped elements oscillate with different average frequencies (Poincare rotation number). We show that imperfect chimera can be realized in simple experiments with mechanical oscillators, namely Huygens clock. The mathematical model of our experiment shows that the observed chimera states are controlled by elementary dynamical equations derived from Newtons laws that are ubiquitous in many physical and engineering systems.

Antiphase synchronization of chaos by noncontinuous coupling: two impacting oscillators

Abstract We show that two identical chaotic oscillators can evolve in antiphase synchronization regime when noncontinuous coupling between them is introduced. As an example, we consider dynamics of two mechanical oscillators coupled by impacts.

Multiscroll Chaotic Sea Obtained from a Simple 3D System Without Equilibrium

Recently, many rare chaotic systems have been found including chaotic systems with no equilibria. However, it is surprising that such a system can exhibit multiscroll chaotic sea. In this paper, a novel no-equilibrium system with multiscroll hidden chaotic sea is introduced. Besides having multiscroll chaotic sea, this system has two more interesting properties. Firstly, it is conservative (which is a rare feature in three-dimensional chaotic flows) but not Hamiltonian. Secondly, it has a coexisting set of nested tori. There is a hidden torus which coexists with the chaotic sea. This new system is investigated through numerical simulations such as phase portraits, Lyapunov exponents, Poincare map, and frequency spectra. Furthermore, the feasibility of such a system is verified through circuital implementation.