We study the evolutions of spatiotemporal chaos for the photorefractive ring oscillator. As the system parameters are
changed, we obtain different patterns such as the frozen random state, the pattern selection state, the defect chaotic
diffusion state and fully developed turbulence state in the one- dimensional map lattice system. We can observe
symmetry breaking from four corners and the boundaries and finally lead to spatiotemporal chaos in the two-dimensional
map lattices system. Then we demonstrate that the global and local constant bias can suppress spatiotemporal chaos in
photorefractive ring oscillator by varying the bias strength. Only if we choose suitable bias strength, spatiotemporal
chaos in photorefractive ring oscillator system can be controlled into stable periodic states.
The chaotic dynamic characteristic in Bose-Einstein Condensate (BEC) system of a 1D tilted optical superlattice potential
with attractive interaction is investigated in this paper. The spatial evolution of chaos was shown numerically by resolving
Gross-Pitaevskii (G-P) equation for the system with the fourth Runge-Kutta(RK) algorithm. Numerical analysis reveals
that as the tilt or the amplitude of the optical superlattice potential is increased the chaos in the BEC system increases. These
elements make the chaotic system more unstable and the phase-space orbit becomes more chaotic. The chaotic system
can be effectively controlled to a stable periodic orbit through adjusting the amplitude of the optical superlattice potential
and initial condition. Controlling chaos can also be realized by spatial constant bias in the BEC system of a 1D tilted optical
superlattice potential with attractive interaction. Phase orbits are suppressed gradually then the chaotic states of the BEC
system are converted into period one through quais-period.
The hyperchaotic orbits in the nonlinear three-wave coupling can be controlled by applying a small control wave. For a given set of linear frequency mismatch and growth-damping parameters, periodic orbit can be achieved by adjusting the amplitude of the control wave. The range of the amplitude of the control wave is determined by calculating the Lyapunov exponent of the three-wave coupling system. Numerical simulations show that the period number differs on the account of the amplitude of the control wave. Increasing the amplitude of the control wave from 0, the hyperchaotic state of the three-wave coupling system results in conversion to periodic 4, subsequently it is converted into period 2, and then into period 1.
Identical synchronization and inverse synchronization of chaos are two basic types of synchronization. In this paper, we present a scheme for identical synchronization and another scheme for inversed synchronization in two degenerate optical parametric oscillators (DOPOs) by mutual couple. For realistic values of the systems, we demonstrate two cases of results as follows. (1) Two independent hyperchaotic systems can go into inversed synchronized hyperchaotic oscillations by mutual couple when the coupling coefficient is in the range 0.12< ε<0.50, or 0.07< ε<0.098; (2) If the two DOPOs are mutually coupled and the coupling coefficient is in the range 0.098< ε<0.12 , they will be controlled to enter into periodic states directly and approach periodic synchronization. They will lose synchronization as the coupling coefficient is smaller than 0.07, but controlling hyperchaos can be realized when the coupling coefficient is near 0.01 and 0.053.
Some aspects of the chaotical dynamics of degenerate optical parametric oscillator(DOPO) were analyzed in this paper. The DOPO exhibits not only nonchaotic but also chaotic or even hyperchaotic behavior according to the amplitude of input field and cavity detuning parameters. To indicate chaotic behavior of the system we make use of the spectrum of lyapunov exponents. The topology of the motion is visualized on the appropriate phase portraits. The chaotic and hyperchaotic behavior of the DOPO can be well controlled to enter into periodicity by modulating the input field.