In this paper, we study bifurcation structures of period-adding phenomena in an internal wave model that is a mathematical model for ocean internal waves. It has been suggested that chaotic solutions observed in the internal wave model may be related to the universal property of the energy spectra of ocean internal waves. In numerical bifurcation analyses of the internal wave model, we illustra...

In this report, we investigate phenomena on the edge of spatially uniform chaotic mode and spatial temporal chaos in a lattice of chaotic 1-D maps with only local connections. It is shown that in autonomous lattice with local connections, spatially uniform chaotic mode cannot exist if the Lyapunov exponent λ of the isolated chaotic map is greater than some critical value λcr > 0. We proposed a ...

The nonlinear and dynamic accommodating capability of time domain models makes them a useful representation of chaotic time series for analysis, modeling and prediction. This paper is devoted to the modeling and prediction of chaotic time series with hidden attractors using a nonlinear autoregressive model with exogenous inputs (NARX) based on a novel recurrent fuzzy functions (RFFs) approach. ...

This paper presents a robust indirect model reference fuzzy control scheme for control and synchronization of chaotic nonlinear systems subject to uncertainties and external disturbances. The chaotic system with disturbance is modeled as a Takagi–Sugeno fuzzy system. Using a Lyapunov function, stable adaptation laws for the estimation of the parameters of the Takagi–Sugeno fuzzy model are deriv...

Shannon wavelet chaotic neural network is a kind of chaotic neural network with non-monotonous activation function composed by Sigmoid and Wavelet. In this paper, wavelet chaotic neural network models with different nonlinear self-feedbacks are proposed and the effects of the different self-feedbacks on simulated annealing are analyzed respectively. Then the proposed models are applied to the 1...

We investigate the origin of diffusion in non-chaotic systems. As an example, we consider 1D map models whose slope is everywhere 1 (therefore the Lyapunov exponent is zero) but with random quenched discontinuities and quasi-periodic forcing. The models are constructed as non-chaotic approximations of chaotic maps showing deterministic diffusion, and represent one-dimensional versions of a Lore...

This paper presents the synchronization of chaotic systems subject to parameter uncertainties. Based on the fuzzy models of chaotic systems, a fuzzy controller is designed to realize chaotic synchronization. A design criterion of the membership functions of fuzzy controller is proposed to facilitate the stability design towards chaotic synchronization when parameter uncertainties are under cons...

A simple approach is proposed to tame chaos by injecting high-frequency signals, commonly called dithers, into the chaotic systems. Based on the relaxed method, an appropriate dither is introduced to suppress chaotic motion. If the frequency of dither is high enough, the trajectory described by the dithered chaotic system and the trajectory of its corresponding mathematical model — the relaxed ...

different methods arising from scientific investigation for removing noise from chaotic signals have been introduced and one of their best is local projection approach. the local projection approach projects the chaotic data in the neighborhood onto the hyper-plane. selection of neighborhood radius has a direct impact on its performance. a noticeable feature associated with chaotic trajectories...