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The present study considers the robust stability for impulsive complex-valued neural networks (CVNNs) with discrete time delays. By applying the homeomorphic mapping theorem and some inequalities in a complex domain, some sufficient conditions are obtained to prove the existence and uniqueness of the equilibrium for the CVNNs. By constructing appropriate Lyapunov-Krasovskii functionals and employing the complex-valued matrix inequality skills, the study finds the conditions to guarantee its global robust stability. A numerical simulation illustrates the correctness of the proposed theoretical results. [ABSTRACT FROM AUTHOR]

In order to comprehend the effects of the duration of pesticide residual effectiveness on successful pest control, a stochastic integrated pest management (IPM) model with pesticides which have residual effects is proposed. Firstly, we show that our model has a global and positive solution and give its explicit expression when pest goes extinct. Then the sufficient conditions for pest extinction combined with the ones for the global attractivity of the pest solution only chemical control are established. Moreover, we also derive sufficient conditions for weak persistence which show that the solution of stochastic IPM models is stochastically ultimately bounded under some conditions. [ABSTRACT FROM AUTHOR]

The main purpose is to develop novel analytical techniques and provide a comprehensive qualitative analysis of global dynamics for a state-dependent feedback control system arising from biological applications including integrated pest management. The model considered consists of a planar system of differential equations with state-dependent impulsive control. We characterize the impulsive and phase sets, using the phase portraits of the planar system and the Lambert W function to define the Poincaré map for impulsive point series defined in the phase set. The existence, local and global stability of an order-1 limit cycle and obtain sharp sufficient conditions for the global stability of the boundary order-1 limit cycle have been provided. We further examine the flip bifurcation related to the existence of an order-2 limit cycle. We show that the existence of an order-2 limit cycle implies the existence of an order-1 limit cycle. We derive sufficient conditions under which any trajectory initiating from a phase set will be free from impulsive effects after finite state-dependent feedback control actions, and we also prove that order- k ( $k\geq3$) limit cycles do not exist, providing a solution to an open problem in the integrated pest management community. We then investigate multiple attractors and their basins of attraction, as well as the interior structure of a horseshoe-like attractor. We also discuss implications of the global dynamics for integrated pest management strategy. The analytical techniques and qualitative methods developed in the present paper could be widely used in many fields concerning state-dependent feedback control. [ABSTRACT FROM AUTHOR]

An expectation for optimal integrated pest management is that the instantaneous numbers of natural enemies released should depend on the densities of both pest and natural enemy in the field. For this, a generalised predator–prey model with nonlinear impulsive control tactics is proposed and its dynamics is investigated. The threshold conditions for the global stability of the pest-free periodic solution are obtained based on the Floquet theorem and analytic methods. Also, the sufficient conditions for permanence are given. Additionally, the problem of finding a nontrivial periodic solution is confirmed by showing the existence of a nontrivial fixed point of the model's stroboscopic map determined by a time snapshot equal to the common impulsive period. In order to address the effects of nonlinear pulse control on the dynamics and success of pest control, a predator–prey model incorporating the Holling type II functional response function as an example is investigated. Finally, numerical simulations show that the proposed model has very complex dynamical behaviour, including period-doubling bifurcation, chaotic solutions, chaos crisis, period-halving bifurcations and periodic windows. Moreover, there exists an interesting phenomenon whereby period-doubling bifurcation and period-halving bifurcation always coexist when nonlinear impulsive controls are adopted, which makes the dynamical behaviour of the model more complicated, resulting in difficulties when designing successful pest control strategies. [ABSTRACT FROM AUTHOR]

The robust stability for the impulsive complex-valued neural networks with mixed time delays is considered in this paper. Based on the homeomorphic mapping theorem, some sufficient conditions are proposed for the existence and uniqueness of the equilibrium point. By constructing appropriate Lyapunov–Krasovskii functions and employing modulus inequality techniques, the global robust stability theorem is obtained for the neural networks in complex domain. Finally, numerical simulations confirm the stability of the system and manifest that the complex-valued neural networks work efficiently on storing and retrieving the image patterns. [ABSTRACT FROM AUTHOR]

There are many challenges to quantifying and evaluating the media impact on the control of emerging infectious diseases. We modeled such media impacts using a piecewise smooth function depending on both the case number and its rate of change. The proposed model was then converted into a switching system, with the switching surface determined by a functional relationship between susceptible populations and different subgroups of infectives. By parameterizing the proposed model with the 2009 A/H1N1 influenza outbreak data in the Shaanxi province of China, we observed that media impact switched off almost as the epidemic peaked. Our analysis implies that media coverage significantly delayed the epidemic's peak and decreased the severity of the outbreak. Moreover, media impacts are not always effective in lowering the disease transmission during the entire outbreak, but switch on and off in a highly nonlinear fashion with the greatest effect during the early stage of the outbreak. The finding draws the attention to the important role of informing the public about 'the rate of change of case numbers' rather than 'the absolute number of cases' to alter behavioral changes, through a self-adaptive media impact switching on and off, for better control of disease transmission. [ABSTRACT FROM AUTHOR]