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In this paper, we investigate the local synchronization problem for delayed phase-coupled oscillators with plastic coupling (also referred as a generalized Kuramoto model). By linearizing the phase-coupled oscillators system at a special solution, an approximation phase-coupled system with delay effects is deduced. Moreover, we find the multiplicity of semisimple zero eigenvalue for coupling strength coefficients matrix and the rank of Vandermonde matrix associated initial values are two sensitive factors. The former is closely related to the maximum number of clusters phase of linear coupled system, and the latter determines clusters phase synchronization. As results, both frequency synchronization criteria and phase synchronization criteria are established in this literature. Also, the final synchronization frequency and phase are formulated in terms of coupling strength, initial values and time delay. [ABSTRACT FROM AUTHOR]

Abstract: The processing delay is incorporated into the influence function of the well-known Cucker–Smale model for self-organized systems with multiple agents. Both symmetric and non-symmetric pairwise influence functions are considered, and a Lyapunov functional approach is developed to establish the existence of flocking solutions for the proposed delayed Cucker–Smale model. An analytic formula is given to calculate the asymptotic flocking velocity in terms of model parameters and the variation of the position during the initial time interval. [Copyright &y& Elsevier]

We consider an age-structured single-species population model in a patch environment consisting of infinitely many patches. Previous work shows that if the nonlinear birth rate is sufficiently large and the maturation time is small, then the model exhibits the usual transition from the trivial equilibrium to the positive (spatially homogeneous) equilibrium represented by a traveling wavefront. Here we show that (i) if the birth rate is so small that a patch alone cannot sustain a positive equilibrium then the whole population in the patchy environment will become extinct, and (ii) if the birth rate is large enough that each patch can sustain a positive equilibrium and if the maturation time is moderate then the model exhibits nonlinear oscillations characterized by the occurrence of multiple periodic traveling waves. [Copyright &y& Elsevier]

We investigate the effects of habitat complexity and multi-time delays on dynamics of a bio-economic predator–prey model. The differential–algebraic system theory is applied to transform the bio-economic model into a normal form, so that the local stability and existence of periodic solutions can be examined by varying the delays and the habitat complexity parameter. The direction of Hopf bifurcation and the stability of bifurcated periodic solutions are investigated. We also discuss the effect of fluctuating environment on dynamical behavior of a corresponding stochastic delayed-differential–algebraic system and derive expressions for intensities of population fluctuations. The model is also used to study the optimal harvesting strategy in order to maximize economic profit while sustaining the ecosystem. Numerical simulations are designed to illustrate the effectiveness of theoretical analysis. [ABSTRACT FROM AUTHOR]

Abstract: The use of combination antiretroviral therapy has proven remarkably effective in controlling HIV disease progression and prolonging survival. However, the emergence of drug resistance can occur. It is necessary that we gain a greater understanding of the evolution of drug resistance. Here, we consider an HIV viral dynamical model with general form of target cell density, drug resistance and intracellular delay incorporating antiretroviral therapy. The model includes two strains: wild-type and drug-resistant. The basic reproductive ratio for each strain is obtained for the existence of steady states. Qualitative analysis of the model such as the well-posedness of the solutions and the equilibrium stability is provided. Global asymptotic stability of the disease-free and drug-resistant steady states is shown by constructing Lyapunov functions. Furthermore, sufficient conditions related to the properties of the target cell density are obtained for the local asymptotic stability of the positive steady state. Numerical simulations are conducted to study the impact of target cell density and intracellular delay focusing on the stability of the positive steady state. The occurrence of Hopf bifurcation of periodic solutions is shown to depend on the target cell density. [Copyright &y& Elsevier]

We consider an artificial neural network where the signal transmission is of a digital (McCulloch–Pitts) nature and is delayed due to the finite switching speed of neurons (amplifiers). For a particular connection topology, we show that all solutions starting from nonoscillatory initial states will be eventually synchronized and stabilized at a unique limit cycle, and hence such a network can be used as a synchronized oscillator. [Copyright &y& Elsevier]

We consider the multiplicity and stability of subharmonic solutions of discrete dynamic systems with periodic perturbations, whose existence was established in the first part of this series. Under the hypotheses that the perturbation is locally Lipschitz continuous, we determine the precise number of subharmonic solutions, and we also show that these subharmonic solutions are stable (unstable) provide the periodic orbit of the unperturbed system is stable (unstable). [Copyright &y& Elsevier]

We consider the existence of subharmonic solutions of systems of difference equations with periodic perturbations. The theory of coincidence degree, coupled with some detailed a priori estimates, is applied to show that the perturbed system admits subharmonic solutions near a hyperbolic periodic orbit of the unperturbed system if the perturbation is sufficiently small. [Copyright &y& Elsevier]

Combining biological and chemical control has been an efficient strategy to combat the evolution of pesticide resistance. Continuous releases of natural enemies could reduce the impact of a pesticide on them and the number to be released should be adapted to the development of pesticide resistance. To provide some insights towards this adaptation strategy, we developed a novel pest–natural enemy model considering both resistance development and inoculative releases of natural enemies. Three releasing functions which ensure the extinction of the pest population are proposed and their corresponding threshold conditions obtained. Aiming to eradicate the pest population, an analytic formula for the number of natural enemies to be released was obtained for each of the three different releasing functions, with emphasis on their biological implications. The results can assist in the design of appropriate control strategies and decision-making in pest management. [ABSTRACT FROM AUTHOR]