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[Display omitted] • A framework is proposed for population-based optimization algorithms' convergence. • DIRECT's partition and population evolutions are repeated in this framework. • The global convergence of the framework is proved. • Framework is applied successfully on three population-based optimization algorithms. Population-based optimization algorithms, such as genetic algorithm and particle swarm optimization, have become a class of important algorithms for solving global optimization problems. However, there is an issue that the global convergence is often absent for most of them. This paper proposes a partition-based convergence framework for population-based optimization algorithms to solve this troubling problem. In this framework, regular partitions and evolutions of populations are implemented alternatively. Specifically, the initial population is generated from a regular partition on the search space; after several generations of evolution of the population, the evolution result is returned to join in the regular partition again, and a new population is generated. Repeat such progress until some stop condition is satisfied. Global convergence is guaranteed for the framework. Then this convergence framework is applied to particle swarm optimization, differential evolution, and genetic algorithm. The modified algorithms are globally convergent and perform better than the original version. [ABSTRACT FROM AUTHOR]

In the paper, to better understand the dynamic relationship between Microcystis aeruginosa and filter-feeding fish, we have constructed a new aquatic ecological model to describe the aggregation effect of Microcystis aeruginosa. Mathematical theory works mainly investigated the critical threshold condition through the discovery of transcritical bifurcation, saddle–node bifurcation, Hopf bifurcation and Bogdanov–Takens bifurcation. The numerical simulation works mainly revealed that Microcystis aeruginosa aggregation effect has played an important role in the dynamic relationship with the aid of bifurcation analysis, which also in turn proved the validity of theoretical derivation. The results showed that if the Microcystis aeruginosa aggregation area became larger and larger, and exceeded a critical threshold, the filter-feeding fish would eventually go extinct. Furthermore, it should be stressed that Microcystis aeruginosa aggregation can effectively control the feeding dynamic behavior of filter-feeding fish and provide shelter from predators. Finally, all these results were expected to be useful in studying population dynamics of some aquatic ecosystems. [ABSTRACT FROM AUTHOR]

• A spatial host-parasite model with frequency- and density-dependent transmissions is developed. • The framework of the existence of the Turing pattern is established. • The model dynamics exhibits a diffusion-controlled formation growth of 'spots, stripes and holes' pattern replication. • The parameters must be adjusted in the specific feasible range to control the disease. The present work is concerned with some fundamental analytic properties of a host-parasite model with frequency- and density-dependent transmissions under homogeneous Neumann boundary condition. The global existence and the boundedness of solution are investigated. The stability of the constant positive steady state is discussed, and the Turing instability is determined. Furthermore, the framework of the occurrence of the Turing pattern of the model is established: when the diffusion coefficients of the susceptible and infected hosts are large enough, there is nonexistence of non-constant positive steady states, which impies that the diffusion is helpful for creating non-constant positive steady states to the model; when the diffusion coefficient of the infected hosts is properly chosen and other parameters are fixed, the model exhibits non-constant positive steady-states, and the stationary Turing pattern can arise as a result of diffusion. Via numerical simulations, the evolutionary processes of the pattern formation of the uninfected/infected hosts with local diffusion are presented, which shows that the model dynamics exhibits a diffusion-controlled formation growth of spots, stripes and holes pattern replication. In the viewpoint of epidemiology, the parameters must be adjusted in the specific feasible range to control the disease. [ABSTRACT FROM AUTHOR]

The nonlinearity degree of the system can be sensitively revealed by the methods based on Nonlinear Output Frequency Response Functions (NOFRFs). However, there is a lack of methods based on NOFRFs that work with only response signals under stochastic excitation, which limits the application of NOFRFs in practical engineering. In this study, a new concept of normalized NOFRFs is proposed, and a corresponding estimation method that employs only stochastic output response is established. Firstly, a method of estimating NOFRFs by Power Spectral Density (PSD) is established, and therefrom the normalized NOFRFs and a corresponding nonlinearity index are proposed. Then, by taking the PSD of the excitation signal as the input and the PSD of the response signal as the output, a general estimation method of normalized NOFRFs is built, and an output measured only estimation method of normalized NOFRFs is further deduced and established. In these two estimation methods, the assumption of white noise excitation is not required, and the estimated results are insensitive to the change of excitation intensity. Finally, the experiments of fatigue damage detection of three-point bending fatigue steel plate specimens and reducer box cases under stochastic excitation are carried out. The results demonstrate that, compared with the NOFRFs, the degree of fatigue damage can be effectively revealed by the normalized NOFRFs with output. • A method for estimating the NOFRFs by PSD is proposed. • Normalized NOFRFs and associated nonlinearity index are proposed. • Output measured only estimation method of normalized NOFRFs is established. • Assumption of white noise excitation is not required in the estimation method. • Fatigue damage can be revealed by normalized NOFRFs as well as the NOFRFs. [ABSTRACT FROM AUTHOR]