一类非光滑Chua’s电路的同步控制

本文研究两个带x|x|非线性项的Chua’s电路的全局指数同步和全局同步的控制问题.证明这两个系统在未加控制时不可能同步,但设计不同的控制器可以实现这两个系统的全局指数同步和全局同步.     

On the domain of fractional Laplacians and related generators of Feller processes

In this paper we study the domain of the generator of stable processes, stable-like processes and more general pseudo- and integro-differential operators which naturally arise both in analysis and as infinitesimal generators of Lévy- and Lévy-type (Feller) processes. In particular we obtain conditions on the symbol of the operator ensuring that certain (variable order) Hölder and Hölder–Zygmund spaces are in the domain. We use tools from probability theory to investigate the small-time asymptotics of the generalized moments of a Lévy or Lévy-type process ${(X_t)}_{t\ge 0}$,

$\underset{t\to 0}{\lim }?\frac{1}{t}({\mathbb{E}}^{x}f(X_t)?f(x)),x\in {\mathbb{R}}^d,$

for functions f which are not necessarily bounded or differentiable. The pointwise limit exists for fixed $x\in {\mathbb{R}}^d$ if f satisfies a Hölder condition at x. Moreover, we give sufficient conditions which ensure that the limit exists uniformly in the space of continuous functions vanishing at infinity. As an application we prove that the domain of the generator of ${(X_t)}_{t\ge 0}$ contains certain Hölder spaces of variable order. Our results apply, in particular, to stable-like processes, relativistic stable-like processes, solutions of Lévy-driven SDEs and Lévy processes.     

Higher integrability for nonlinear elliptic equations with variable growth and discontinuous coefficients

In this paper, based on the theory of variable exponent spaces, we study the higher integrability for a class of nonlinear elliptic equations with variable growth and discontinuous coefficients. Under suitable assumptions, we obtain a local gradient estimate in Orlicz space for weak solution.     

Boundary value problems for a quasilinear parabolic equation with an unknown coefficient

The work is connected with the mathematical modeling of physical–chemical processes in which inner characteristics of materials are subjected to changes. The considered nonlinear parabolic models consist of a boundary value problem for a quasilinear parabolic equation with an unknown coefficient multiplying the derivative with respect to time and, moreover, involve an additional relationship for a time dependence of this coefficient. For such a system, conditions of unique solvability in a class of smooth functions are studied on the basis of the Rothe method. The proposed approach involves the proof of a priori estimates in the difference-continuous Hölder spaces for the corresponding differential-difference nonlinear system that approximates the original system by the Rothe method. These estimates allow one to establish the existence of the smooth solutions and to obtain the error estimates of the approximate solutions.As examples of applications of the considered nonlinear boundary value problems, the models of destruction of heat-protective composite under the influence of high temperature heating are discussed.     

A novel hyperchaotic system and its circuit implementation

A four-dimensional hyperchaotic system with five parameters is proposed. Its dynamical properties such as dissipativity, equilibrium points, Lyapunov exponent, Lyapunov dimension, bifurcation diagrams and Poincare maps are analyzed theoretically and numerically. Theoretical analyses and simulation tests indicate that the new system's dynamics behavior can be periodic attractor, chaotic attractor and hyperchaotic attractor as the parameter varies. Finally, the circuit of this new hyperchaotic system is designed and realized by Multisim software. The simulation results confirm that the chaotic system is different from the existing chaotic systems and is a novel hyperchaotic system. The system is recommendable for many engineering applications such as information processing, cryptology, secure communications, etc.     

On Applications of Quasi-Monotone Sequences and Quasi Power Increasing Sequences

In this article, we prove a general theorem dealing with an application of quasi-f-power increasing sequences and δ-quasi monotone sequences. This theorem also includes some known and new results.     

Multiple positive solutions for Schrödinger‐Poisson system involving singularity and critical exponent

In this paper, the existence and multiplicity of positive solutions is established for Schrödinger‐Poisson system of the form where 0 ∈ Ω is a smooth bounded domain in , , and λ > 0 is a real parameter. Combining with the variational method and Nehari manifold method, two positive solutions of the system are obtained.     

Evaluating nonlinear variability of mental fatigue behavioral indices during long‐term attentive task

This study investigates the behavioral indices of attention. A simple repetitive attentive task that resulted in mental fatigue was used consecutively in four trials. In the first step, reaction time and error responses were recorded to evaluate differences among trials. During the task, subjects showed different responses to stimulations. In the second part, to recognize the strategies, multiple clustering methods such as k‐means and fuzzy c‐means were performed in which behavioral indices and nonlinear features were used. In the last section, mental behavior was identified as a result of the chaotic properties of variations in reaction time. Therefore, the Lyapunov exponent of reaction times was evaluated. Results revealed that behavioral indices could distinguish attention from the occurrence of mental fatigue in trials. In addition, the three strategies used by subjects during the test protocol were assessed. Finally, variation of indices extracted from nonlinear analysis, that is, decrease in degree of chaotic behavior determined the transition from attention to mental fatigue. © 2012 Wiley Periodicals, Inc. Complexity, 2012