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The nonlinear dynamics and control of micro electromechanical systems (MEMS) is an important topic at present and homotopy analysis method (HAM) is an effective semi-numerical and semi-analytical method for solving strongly nonlinear problems. In this paper, the parametric resonance of MEMS with multi-frequency excitation is studied by HAM. Firstly, the differential equation of electrostatically driven microbeam is processed by Taylor expansion, and it is transformed into the parametric motion model with multi-frequency excitation. Then, the approximate solution and amplitude–frequency response equation of the system are obtained by HAM, and compared with the numerical solution. Finally, the influence of direct current (DC) and alternating current (AC) on principal parametric resonance and superharmonic resonance is discussed. The results show that HAM is an effective method to analyze the parametric vibration of multi-frequency excitation system, and the amplitude–frequency response curve of microbeam about parametric motion depends on the time scale in high DC and high AC state. This study effectively extends the application of HAM in parametric resonance, which is of great significance to the study of nonlinear vibration of MEMS. • HAM is first used to analyze resonance under multi-frequency excitation. • Softening and hardening effect of microbeam depends on time. • Primary and superharmonic resonance of MEMS are further considered. • HAM is an effective method to study the multi-frequency excitation. [ABSTRACT FROM AUTHOR]

Recently, much progress has been made on particle swarm optimization (PSO). A number of works have been devoted to analyzing the convergence of the underlying algorithms. Nevertheless, in most cases, rather simplified hypotheses are used. For example, it often assumes that the swarm has only one particle. In addition, more often than not, the variables and the points of attraction are assumed to remain constant throughout the optimization process. In reality, such assumptions are often violated. Moreover, there are no rigorous rates of convergence results available to date for the particle swarm, to the best of our knowledge. In this paper, we consider a general form of PSO algorithms, and analyze asymptotic properties of the algorithms using stochastic approximation methods. We introduce four coefficients and rewrite the PSO procedure as a stochastic approximation type iterative algorithm. Then we analyze its convergence using weak convergence method. It is proved that a suitably scaled sequence of swarms converge to the solution of an ordinary differential equation. We also establish certain stability results. Moreover, convergence rates are ascertained by using weak convergence method. A centered and scaled sequence of the estimation errors is shown to have a diffusion limit. [ABSTRACT FROM AUTHOR]

Abstract: Here we present a new hybrid genetic algorithm (HGA) with the Baldwin effect. In the HGA, a local search is employed to change the fitness of individuals but the acquired improvements do not change the individual itself. This local search step exploits the Baldwin effect. Some numerical applications show that this algorithm can yield the global optimum more efficiently than commonly used HGAs. A theorem is presented that guarantees the convergence in probability of the new HGA. [Copyright &y& Elsevier]

Abstract: A class of new simple Hopfield neural networks is revisited. To confirm the chaotic behavior in these Hopfield neural networks demonstrated in numerical studies, we resort to Poincaré section and Poincaré map technique and present a rigorous verification of existence of horseshoe chaos by virtue of topological horseshoes theory and estimates of topological entropy in the derived Poincaré maps. [Copyright &y& Elsevier]

Maximizing modularity is a widely used method for community detection, which is generally solved by approximate or greedy search because of its high complexity. In this paper, we propose a method, named MSM, for modularity maximization, which reformulates the modularity maximization problem as a subset identification problem and maximizes the surrogate of the modularity. The surrogate of the modularity is constructed by replacing the discontinuous indicator functions in the reformulated modularity function with the continuous truncated L 1 function. This makes the NP-hard problem of maximizing the modularity function approximately become a non-convex optimization problem, which can be efficiently solved via the DC (Difference of Convex Functions) Programming. The proposed MSM method can be used for community detection when the number of communities is given, and it can also be applied to the situation where the number of communities is unknown. Then, we demonstrate the advantages of the proposed MSM method by some simulation results and real data analyses. [ABSTRACT FROM AUTHOR]