Chaos generation via a switching fractional multi-model system

This paper introduces a system with switching multi-model structure which can generate chaos. Sub-models in this structure are fractional-order linear systems with any desired commensurate order less than 1. It shows that this system is capable of demonstrating chaotic behavior if its parameters and switching rule are suitably chosen. The structure of the proposed system is defined in a general form; consequently various chaotic attractors can be created by this system with different choices of order, parameters and switching rule. Numerical simulations illustrate behavior of the introduced system in some different situations.     

Sparse principal component regression via singular value decomposition approach

Advances in Data Analysis and Classification - Principal component regression (PCR) is a two-stage procedure: the first stage performs principal component analysis (PCA) and the second stage builds...     

Existence and multiple solutions for a second-order difference boundary value problem via critical point theory

In this paper, the critical point theory is employed to establish existence and multiple solutions for a second-order difference boundary value problem.     

Robust synchronization for stochastic delayed complex networks with switching topology and unmodeled dynamics via adaptive control approach

In this paper, the robust synchronization problem for a class of stochastic delayed complex networks with switching topology and unmodeled dynamics is investigated by using the adaptive control scheme. Different from some existing uncertain complex network models, the uncertain terms in the complex networks are only needed to be bounded. Based on the stability theory of stochastic delayed differential equation, a novel adaptive controller which ensures that all the nodes in the complex networks robustly synchronize with the target node is derived. Finally, a numerical example is provided to show the effectiveness of the proposed method.     

Uniform attractor for non-autonomous plate equation with a localized damping and a critical nonlinearity

In this paper, we consider dynamical behavior of non-autonomous plate-type evolutionary equations with critical nonlinearity. We prove the existence of a uniform attractor in the space .     

Multiplicity result for some nonlocal anisotropic equation via nonsmooth critical point theory approach

In this paper we study quasilinear problems involving variable exponent growth conditions and nonlocal terms on the whole space R^N. A multiplicity result is established. All the coefficients involved in the terms of the equation depend both on the variable x and the unknown function u. Our main argument is nonsmooth critical point theory.     

MILP approach to pattern generation in logical analysis of data

Pattern generation methods for the Logical Analysis of Data (LAD) have been term-enumerative in nature. In this paper, we present a Mixed 0-1 Integer and Linear Programming (MILP) approach that can identify LAD patterns that are optimal with respect to various previously studied and new pattern selection preferences. Via art of formulation, the MILP-based method can generate optimal patterns that also satisfy user-specified requirements on prevalence, homogeneity and complexity. Considering that MILP problems with hundreds of 0-1 variables are easily solved nowadays, the proposed method presents an efficient way of generating useful patterns for LAD. With extensive experiments on benchmark datasets, we demonstrate the utility of the MILP-based pattern generation.     

Bifurcation analysis of the Zhukovskii-Volterra system via bi-Hamiltonian approach

The main goal of this paper consists of bifurcation analysis of classical integrable Zhukovskii-Volterra system. We use the fact that the ZV system is bi-Hamiltonian and apply new techniques [1] for analysis of singularities of bi-Hamiltonian systems, which can be formulated as follows: the structure of singularities of a bi-Hamiltonian system is determined by that of the corresponding compatible Poisson brackets.     

Chaotic fractional-order Coullet system: Synchronization and control approach

The main objective of this study is to investigate and control the chaotic behaviour of fractional-order Coullet system, including the necessary condition for appearance of chaos. An active control technique, in a master–slave structure for synchronization is suggested to control this chaotic system. The stability condition is obtained in both of theoretical analysis and simulation manner. The numerical simulation verifies the performance of the proposed controller.     

A value of information in FLP problems via sensitivity analysis

A Fuzzy Linear Programming (FLP) Problem is formulated and the value of information is discussed. If the fuzziness of coefficients is decreased by using information about the coefficients, we can expect to obtain a more satisfactory solution than without information. With this view, the prior value of information is discussed. Using the sensitivity analysis technique, a method of allocating the given investigation cost to each fuzzy coefficient is proposed.     

A simple approach to fuzzy critical path analysis in project networks

This paper develops a simple approach to critical path analysis in a project network with activity times being fuzzy numbers. The idea is based on the linear programming (LP) formulation and fuzzy number ranking method. The fuzzy critical path problem is formulated as an LP model with fuzzy coefficients of the objective function, and then on the basis of properties of linearity and additivity, the Yager’s ranking method is adopted to transform the fuzzy LP formulation to the crisp one which can be solved by using the conventional streamlined solution methods. Consequently, the critical path and total duration time can be obtained from the derived optimal solution. Moreover, in this paper we also define the most critical path and the relative path degree of criticality, which are theoretically sound and easy to use in practice. An example discussed in some previous studies illustrates that the proposed approach is able to find the most critical path, which is proved to be the same as that derived from an exhausted comparison of all possible paths. The proposed approach is very simple to apply, and it is not require knowing the explicit form of the membership functions of the fuzzy activity times.     

Nontrivial solutions for discrete boundary value problems with multiple resonance via computations of the critical groups

In this paper, we study the existence of nontrivial solutions for a class of second-order difference equations with multiple resonance at both infinity and the origin by applying the critical point theory and Morse theory.     

Existence and multiplicity of solutions for an impulsive boundary value problem with a parameter via critical point theory

In this paper, an impulsive boundary value problem with a parameter is considered. By using critical point theory, some criteria are obtained to guarantee that the impulsive problem has at least one solution, two solutions and infinitely many solutions when the parameter lies in different intervals. The results obtained are also valid and new for a problem discussed in the literature.     

A new approach to constrained optimization via image space analysis

In this article, by introducing a class of nonlinear separation functions, the image space analysis is employed to investigate a class of constrained optimization problems. Furthermore, the equivalence between the existence of nonlinear separation function and a saddle point condition for a generalized Lagrangian function associated with the given problem is proved.     

Multiple solutions for a fourth-order difference boundary value problem with parameter via variational approach

By establishing the corresponding variational framework, and using the mountain pass theorem, linking theorem and Clark theorem in critical point theory, we give the existence of multiple solutions for a fourth-order difference boundary value problem with parameter. Under some suitable assumptions we obtain some results which ensure the existence of well precise interval of parameter for which the problem admits multiple solutions. Some examples are presented to illustrate the main results.     

Multiple solutions of boundary value problems: an elementary approach via the shooting method

In this paper we derive the existence of multiple solutions for boundary value problems of the type $$u\prime \prime + f\left( {t,u} \right) = 0,u\left( 0 \right) = 0,u\left( \pi \right) = 0$$ , in terms of the behaviour of the ratiof(t,u)/u nearu=0 and near infinity. The nonlinear termf is assumed to be locally Lipschitz inu, so that the shooting method can be used. (AMS Subject Classification: 34B15).