Switching adaptive controllers to control fractional‐order complex systems with unknown structure and input nonlinearities

This article investigates the chaos control problem for the fractional‐order chaotic systems containing unknown structure and input nonlinearities. Two types of nonlinearity in the control input are considered. In the first case, a general continuous nonlinearity input is supposed in the controller, and in the second case, the unknown dead‐zone input is included. In each case, a proper switching adaptive controller is introduced to stabilize the fractional‐order chaotic system in the presence of unknown parameters and uncertainties. The control methods are designed based on the boundedness property of the chaotic system's states, where, in the proposed methods the nonlinear/linear dynamic terms of the fractional‐order chaotic systems are assumed to be fully unknown. The analytical results of the mentioned techniques are proved by the stability analysis theorem of fractional‐order systems and the adaptive control method. In addition, as an application of the proposed methods, single input adaptive controllers are adopted for control of a class of three‐dimensional nonlinear fractional‐order chaotic systems. And finally, some numerical examples illustrate the correctness of the analytical results. © 2014 Wiley Periodicals, Inc. Complexity 21: 211–223, 2015     

Modeling and analysis of a marine plankton system with nutrient recycling and diffusion

This article describes a nutrient‐phytoplankton‐zooplankton system with nutrient recycling in the presence of toxicity. We have studied the dynamical behavior of the system with delayed nutrient recycling in the first part of the article. Uniform persistent of the system is examined. In the second part of the article, we have incorporated diffusion of the plankton population to the system and dynamical behavior of the system is analyzed with instantaneous nutrient recycling. The condition of the diffusion driven instability is obtained. The conditions for the occurrence of Hopf and Turing bifurcation critical line in a spatial domain are derived. Variation of the system with small periodicity of diffusive coefficient has been studied. Stability condition of the plankton system subject to the periodic diffusion coefficient of the zooplankton is derived. It is observed that nutrient‐phytoplankton‐zooplankton interactions are very complex and situation specific. Moreover, we have obtained different exciting results, ranging from stable situation to cyclic oscillatory behavior may occur under different favorable conditions, which may give some insights for predictive management. © 2014 Wiley Periodicals, Inc. Complexity 21: 229–241, 2015     

Ideological Complex Systems: Mathematical Theory

The goal of this article is to build an abstract mathematical theory rather than a computational one of the process of transmission of ideology. The basis of much of the argument is Patten's Environment Theory that characterizes a system with its double environment (input or stimulus and output or response) and the existing interactions among them. Ideological processes are semiotic processes, and if in Patten's theory, the two environments are physical, in this theory ideological processes are physical and semiotic, as are stimulus and response. © 2014 Wiley Periodicals, Inc. Complexity 21: 47–65, 2015     

On the structure of split Leibniz triple systems

We study the structure of arbitrary split Leibniz triple systems with a coherent 0-root space. By developing techniques of connections of roots for this kind of triple systems, under certain conditions, in the case of T being of maximal length, the simplicity of the Leibniz triple systems is characterized.     

Homoclinic orbits for first order Hamiltonian systems with some twist conditions

In this paper, we study the nonperiodic first-order Hamiltonian system ù = J L(t)u +J H(t, u), where H ∈ C1(R × R2n). With some assumptions on L, the corresponding Hamiltonian operator has only discrete spectrum. By using the index theory for self-adjoint operator equation,we establish the existence of multiple homoclinic orbits for the asymptotically quadratic nonlinearty satisfying some twist conditions between infinity and origin.     

Robust sampled‐data H∞ control for mechanical systems

This article addresses the issue of robust sampled‐data control for a class of uncertain mechanical systems with input delays and linear fractional uncertainties which appear in all the mass, damping, and stiffness matrices. Then, a novel Lyapunov–Krasovskii functional is constructed to obtain sufficient conditions under which the uncertain mechanical system is robustly, asymptotically stable with disturbance attenuation level about its equilibrium point for all admissible uncertainties. More precisely, Schur complement and Jenson's integral inequality are utilized to substantially simplify the derivation of the main results. In particular, a set of sampled‐data controller is designed in terms of the solution of certain linear matrix inequalities that can be solved effectively using available MATLAB software. Finally, a numerical example with simulation result is provided to show the effectiveness and less conservativeness of the proposed sampled‐data control scheme. © 2014 Wiley Periodicals, Inc. Complexity 20: 19–29, 2015     

Dynamic output feedback consensus of continuous‐time networked multiagent systems

This article addresses the dynamic output feedback consensus problem of continuous‐time networked multiagent systems. Both a fixed topology and Markovian switching topologies are considered. The consensus algorithms are on the base of the output information of each agent's itself and its neighbors. Some sufficient conditions for consensus of multiagent systems are obtained in forms of bilinear matrix inequalities. The algorithm based on the homotopy continuation method is given to compute the feasible controller gains. Numerical simulations are given to show the effectiveness of the proposed results. © 2014 Wiley Periodicals, Inc. Complexity 20: 35–42, 2015     

Parametric inference for multiple repairable systems under dependent competing risks

The focus of this article is on the analysis of repairable systems that are subject to multiple sources of recurrence. The event of interest at the system level is assumed to be caused by the earliest occurrence of a source, thereby conforming to a series system competing risks framework. Parametric inference is carried out under the power law process model that has found significant attention in industrial applications. Dependence among the cause‐specific recurrent processes is induced via a shared frailty structure. The theoretical inference results are implemented to a warranty database for a fleet of automobiles, for which the warranty repair is triggered by the failure of one of many components. Extensive finite‐sample simulation is carried out to supplement the asymptotic findings. Copyright © 2014 John Wiley & Sons, Ltd.     

Enormously extended π-electronic conjugation system of dimeric octaethylporphyrin transmitted with anthracene

Based on the fact that anthracene (Anth) possesses much higher similarity in electron-releasing ability to porphyrin nucleus than the other polyacenes, the dimeric octaethylporphyrin (OEP) derivatives 4 and 5 (OEP–Anth–OEP) were synthesized and their structure–property relationships were examined, as compared with related OEP dimers 1–3. Among them, the derivative 4 showed enormously high electronic communication between two terminal OEP rings, potentially providing a suitable unit of the electronic structure for molecular design of the OEP devices operating with less energy and with higher sensitivity to outside stimuli.     

Cucurbit[7]uril promoting PdCl2-catalyzed cross-coupling reaction of benzyl halides and arylboronic acids in aqueous media

The research provides a novel approach for producing diarylmethane derivatives using CB[7]–NaCl–PdCl₂ catalyzed Suzuki cross-coupling reaction of benzyl chloride derivatives and arylboronic acids in ethanol aqueous solution.