| 概要 | I.
Dynamical systems in the real domain are currently one of the most popular areas of scientific study. There is, however, a wide variety of physical problems, which, from mathematical point of view, can be more conveniently studied using complex variables. In this talk, I will focus on some complex nonlinear systems which are appeared in several important applications in applied sciences. The dynamics of these systems is rich in the sense that our systems exhibit both chaotic and hyperchaotic attractors as well as periodic, quasi-periodic solutions and solutions that approach fixed points. The stability analysis of fixed points will be stated. Numerically the range of parameters values of these systems at which chaotic and hyperchaotic attractors exist is calculated. Lyapunov exponents are computed to classify the dynamics of these systems. Symmetry, invariance and dissipation are discussed.
II.
Chaos and hyperchaos synchronization are important problems in the nonlinear science. Chaos (or hyperchaos) synchronization refers to a process wherein two (or more than two) chaotic (or hyperchaotic) systems (either identical or different) adjust a given property of their motion to a common behavior due to coupling or forcing. I will review, in this talk, several types of synchronization features: complete synchronization (CS), anti-synchronization (AS), projective synchronization (PS), modified projective synchronization (MPS) and lag synchronization (LS,) of some complex nonlinear dynamical systems. The stability analysis of the error dynamical systems is studied. Chaos control of these complex systems is investigated by adding a complex periodic forcing. Lyapunov exponents are calculated to prove that that the chaotic (or hyperchaotic) behavior is converted to periodic one. |