Partial Chaos Research Articles

Application of Fuzzy Controller Based on Chaos Optimal Design

It is difficult to tune parameters of fuzzy controller (FC), and control rules and membership functions of FC are hard to obtain optimization too.Therefore, the control results show strong overshoot and oscillation often.The authors propose a chaos optimal design method based on annealing strategy.According to random and ergodic features of chaos dynamics, the chaotic variables are applied to searching for parameters of FC, the optimal variables are transformed into chaotic variables by carrier-wave, the global search process is done using ergodic features of chaotic motion, and then an approximate global optimal solution is obtained. After that, the chaos local searching and optimization based on annealing strategy is cited, the parameters are optimized again within the limits of the approximate global optimal solution, which is realized by means of combination of global and partial chaos searching, which can converge quickly to global optimal value.Finally, simulations of third order and nonlinear system show that control result of the method is good.

Weak universality for a class of 3d stochastic reaction–diffusion models

We establish the large scale convergence of a class of stochastic weakly nonlinear reaction-diffusion models on a three dimensional periodic domain to the dynamic Phi^3_4 model within the framework of paracontrolled distributions. Our work extends previous results of Hairer and Xu to nonlinearities with a finite amount of smoothness (in particular C^9 is enough). We use the Malliavin calculus to perform a partial chaos expansion of the stochastic terms and control their L^p norms in terms of the graphs of the standard Phi^3_4 stochastic terms.

Topological chaos: what may this mean?

We confront existing definitions of chaos with the state of the art in topological dynamics. The article does not propose any new definition of chaos but, starting from several topological properties that can be reasonably called chaotic, tries to sketch a theoretical view of chaos. Among the main ideas in this article are the distinction between overall chaos and partial chaos, and the fact that some dynamical properties may be considered more chaotic than others.

Complete and generalized chaotic synchronization in a system of three interacting maps

The bifurcation decay of complete chaos synchronization and the mechanisms of transition to partial synchronization of regular and chaotic oscillations are considered in a ring of three logistic maps with symmetric diffusion coupling. The modes of partial chaos synchronization are shown to be at the same time the modes of generalized chaotic synchronization.

Chaotic turing pattern formation in spatiotemporal systems

The problem of Turing pattern formation has attracted much attention in nonlinear science as well as physics, chemistry and biology. So far spatially ordered Turing patterns have been observed in stationary and oscillatory media only. In this paper we find that spatially ordered Turing patterns exist in chaotic extended systems. And chaotic Turing patterns are strikingly rich and surprisingly beautiful with their space structures. These findings are in sharp contrast with the intuition of pseudo-randomness of chaos. The richness and beauty of the chaotic Turing patterns are attributed to a large variety of symmetry properties realized by various types of self-organizations of partial chaos synchronizations.

Fuzzy controller based on chaos optimal design and its application

In order to overcome difficulty of tuning parameters of fuzzy controller, a chaos optimal design method based on annealing strategy is proposed. First, apply the chaotic variables to search for parameters of fuzzy controller, and transform the optimal variables into chaotic variables by carrier-wave method. Making use of the intrinsic stochastic property and ergodicity of chaos movement to escape from the local minimum and direct optimization searching within global range, an approximate global optimal solution is obtained. Then, the chaos local searching and optimization based on annealing strategy are cited, the parameters are optimized again within the limits of the approximate global optimal solution, the optimization is realized by means of combination of global and partial chaos searching, which can converge quickly to global optimal value. Finally, the third order system and discrete nonlinear system are simulated and compared with traditional method of fuzzy control. The results show that the new chaos optimal design method is superior to fuzzy control method, and that the control results are of high precision, with no overshoot and fast response.

Regularity–Partial Chaos–Regularity Transition and Overlapped KAM Scenarios in a Conservative System of Two Linearly Coupled Double-Well Oscillators

For linearly coupled double-well oscillators the regularity–partial chaos–regularity transition is found. First, an incomplete KAM scenario develops with increasing energy, from integrable pattern comprising in-phase and out-of-phase small elliptic orbits towards a partial chaos, with a deformed regular island immersed in a chaotic sea. At a critical energy a new deformed island appears as a mirror image. Above the critical energy the inverse KAM scenario leads to gradual destruction of partial chaos and to the appearance of large elliptic orbits which correspond to the large-amplitude limit governed by uncoupled oscillators with cubic anharmonicities.

DIFFUSIVE CUT-OFF SCALE OF FRACTAL SURFACES IN CHAOTIC MIXING

Results concerning the fractal properties of isovalue surfaces of a passive, diffusive scalar field being advected by a three-dimensional, steady flow exhibiting chaotic streamlines are presented. For all the Péclet numbers and the flow fields studied, the mixing efficiency is shown to be related to the extent of the so-called advective zone for which the similarity dimension Ds is optimal in the sense of mixing (Ds=3). For global chaos, the effective mixing time can be related to the diffusive cut-off scale which bounds this zone. For partial chaos, this cut-off scale corresponds to the size of the regular region which limits asymptotically the mixing.