Chaos is a special feature of complex parametric nonlinear dynamical systems. It has the random-like behavior usually seen in stochastic systems although it is associated with deterministic dynamics. Chaos is at the edge of stability and therefore could easily lead systems to an unstable, performance-degraded, or even catastrophic situation. In such cases, chaos is considered as undesired and s...

We present a method for linear stability analysis of systems with parametric uncertainty formulated in the stochastic Galerkin framework. Specifically, we assume that model partial differential equation, parameter is given form generalized polynomial chaos expansion. The leads to solution eigenvalue problem, and wish characterize rightmost eigenvalue. focus, particular, on problems nonsymmetric...

We perform an experimental parametric study of the chaos generated by a laser diode subjected to phase-conjugate feedback. In addition typical figure merit, i.e., bandwidth, corresponding spectral flatness and permutation entropy at delay is analyzed. Our observations reveal that can be with bandwidth $\ensuremath{\approx}29$ GHz, up 0.75, 0.99. These optimized performances are maintained over ...

We report on an experimental observation of optical wave chaos in a resonator consisting of three standard, high-reflectivity mirrors. The nonseparability of the wave equation necessary for chaos is introduced by violating the paraxial approximation. Until recently progress in optical wave chaos was hampered by the inherent difficulty in realizing suitable microscopic systems; now this novel, m...

This paper formulates a new approach to the study of chaos in discrete dynamical systems based on the notions of inverse ill-posed problems, set-valued mappings, generalized and multivalued inverses, graphical convergence of a net of functions in an extended multifunction space (Sengupta and Ray, 2000), and the topological theory of convergence. Order, chaos, and complexity are described as dis...

A significant progress has been made towards characterizing non-Gaussian state density function. Two new methods adaptive Gaussian mixture model (AGMM) and conjugate unscented transformation (CUT) have been developed for this purpose. AGMM method solves the Fokker-Planck-Kolmogorov equation associated with orbital dynamics model. Furthermore, sparse approximation tools have been used to identif...

This paper surveys frequency-domain and time-domain methods for feedback nonlinear systems and their possible applications to chaos control, coupled systems and complex dynamical networks. The absolute stability of Lur’e systems with single equilibrium and global properties of a class of pendulum-like systems with multi-equilibria are discussed. Time-domain and frequency-domain criteria for the...

We carried out a fluid dynamical simulation for a forced dripping faucet system using a new algorithm that was recently developed. The simulation shows that periodic external forcing induces transitions from chaotic to periodic motion and vice versa. We further constructed an improved mass-sprig model for the same system on the basis of data obtained from the fluid dynamical computations. A det...

This paper surveys some recent results about chaos induced by snap-back repellers and its applications to anti-control of chaos (or, chaotification). Several criteria of chaos induced by snap-back repellers in finite and infinite dimensional dynamical systems are introduced. Some successful applications are given to chaotification problems for finite and infinitedimensional discrete dynamical s...

This paper presents anti-synchronization of two different chaotic systems using optimal control method. The proposed technique is applied to achieve chaos anti-synchronization for the new fourdimensional and hyperchaotic Lü systems with fully unknown parameters. Numerical simulations results are presented to demonstrate the effectiveness of the method.