We analyze the chaotic motion and its shape dependence in a piecewise linear map using Fujisaka's characteristic function method. The map is a generalization of the one introduced by Artuso. Exact expressions for diffusion coefficients are obtained with previously obtained results used as special cases. A fluctuation spectrum relating to the probability density function is obtained in a paramet...

chaotic systems are nonlinear dynamic systems, the main feature of which is high sensitivity to initial conditions. to initiate a design process in fuzzy model, chaotic systems must first be represented by t-s fuzzy models. in this paper, a new fuzzy modeling method based on sector nonlinearity approach has been recommended for chaotic systems relating to initial condition variations using the ...

Let ρ(x, t) denote a family of probability density functions parameterized by time t. We show the existence of a family {τt : t > 0} of deterministic nonlinear (chaotic) point transformations whose invariant probability density functions are precisely ρ(x, t). In particular, we are interested in the densities that arise from the diffusions. We derive a partial differential equation whose soluti...

Analysis of nonlinear autonomous systems has been a popular field of study in recent decades. As an interesting nonlinear behavior, chaotic dynamics has been intensively investigated since Lorenz discovered the first physical evidence of chaos in his famous equations. Although many chaotic systems have been ever reported in the literature, a systematic and qualitative approach for chaos generat...

This paper overviews nonlinear dynamics of switching power converters which are common objects in dynamical system theory and power electronics. First, complex dynamics of single switching power converters is discussed. Their nonlinear switching can cause rich chaotic and bifurcation phenomena including complicated superstable periodic behavior in discontinuous conduction mode. Second, parallel...

In this paper, we propose a digitalized chaotic map, Variational Logistic Map (VLM), modified from classical logistic map to be used in secure communication. Compared with classical logistic map, VLM has large parameter space without windows and can be implemented at low hardware cost. Referring to statistical testing suites SP800-22 and TestU01, VLM with the proposed scrambling method can sign...

We show on the example of the Arnold cat map that classical chaotic systems can be simulated with exponential efficiency on a quantum computer. Although classical computer errors grow exponentially with time, the quantum algorithm with moderate imperfections is able to simulate accurately the unstable chaotic classical nonlinear dynamics for long times. The algorithm can be easily implemented o...