An Impulsive Three-Species Model with Square Root Functional Response and Mutual Interference of Predator

An impulsive two-prey and one-predator model with square root functional responses, mutual interference, and integrated pest management is constructed. By using techniques of impulsive perturbations, comparison theorem, and Floquet theory, the existence and global asymptotic stability of prey-eradication periodic solution are investigated. We use some methods and sufficient conditions to prove the permanence of the system which involve multiple Lyapunov functions and differential comparison theorem. Numerical simulations are given to portray the complex behaviors of this system. Finally, we analyze the biological meanings of these results and give some suggestions for feasible control strategies

The effects of resource limitation on a predator-prey model with control measures as nonlinear pulses

The dynamical behavior of a Holling II predator-prey model with control measures as nonlinear pulses is proposed and analyzed theoretically and numerically to understand how resource limitation affects pest population outbreaks. The threshold conditions for the stability of the pest-free periodic solution are given. Latin hypercube sampling/partial rank correlation coefficients are used to perform sensitivity analysis for the threshold concerning pest extinction to determine the significance of each parameter. Comparing this threshold value with that without resource limitation, our results indicate that it is essential to increase the pesticide’s efficacy against the pest and reduce its effectiveness against the natural enemy, while enhancing the efficiency of the natural enemies. Once the threshold value exceeds a critical level, both pest and its natural enemies populations can oscillate periodically. Furthermore,when the pulse period and constant stocking number as a bifurcation parameter, the predator-prey model reveals complex dynamics. In addition, numerical results are presented to illustrate the feasibility of our main results

An Impulsive Two-Prey One-Predator System with Seasonal Effects

In recent years, the impulsive population systems have been studied by many researchers. However, seasonal effects on prey are rarely discussed. Thus, in this paper, the dynamics of the Holling-type IV two-competitive-prey one-predator system with impulsive perturbations and seasonal effects are analyzed using the Floquet theory and comparison techniques. It is assumed that the impulsive perturbations act in a periodic fashion, the proportional impulses (the chemical controls) for all species and the constant impulse (the biological control) for the predator at different fixed time but, the same period. In addition, the intrinsic growth rates of prey population are regarded as a periodically varying function of time due to seasonal variations. Sufficient conditions for the local and global stabilities of the two-prey-free periodic solution are established. It is proven that the system is permanent under some conditions. Moreover, sufficient conditions, under which one of the two preys is extinct and the remaining two species are permanent, are also found. Finally, numerical examples and conclusion are given

Optimum timing for integrated pest management: Modelling rates of pesticide application and natural enemy releases

Many factors including pest natural enemy ratios, starting densities, timings of natural enemy releases, dosages and timings of insecticide applications and instantaneous killing rates of pesticides on both pests and natural enemies can affect the success of IPM control programmes. To address how such factors influence successful pest control, hybrid impulsive pest–natural enemy models with different frequencies of pesticide sprays and natural enemy releases were proposed and analyzed. With releasing both more or less frequent than the sprays, a stability threshold condition for a pest eradication periodic solution is provided. Moreover, the effects of times of spraying pesticides (or releasing natural enemies) and control tactics on the threshold condition were investigated with regard to the extent of depression or resurgence resulting from pulses of pesticide applications. Multiple attractors from which the pest population oscillates with different amplitudes can coexist for a wide range of parameters and the switch-like transitions among these attractors showed that varying dosages and frequencies of insecticide applications and the numbers of natural enemies released are crucial. To see how the pesticide applications could be reduced, we developed a model involving periodic releases of natural enemies with chemical control applied only when the densities of the pest reached the given Economic Threshold. The results indicate that the pest outbreak period or frequency largely depends on the initial densities and the control tactics

Modelling and Analysis of a Pest-Control Pollution Model with Integrated Control Tactics

A hybrid impulsive pest control model with stage structure for pest and Holling II functional response is proposed and investigated, in which the effects of impulsive pesticide input in the environment and in the organism are considered. Sufficient conditions for global attractiveness of the pest-extinction periodic solution and permanence of the system are obtained, which show that there exists a globally asymptotically stable pest-extinction periodic solution when the number of natural enemies released is more than some critical value, whereas the system can be permanent when the number of natural enemies released is less than another critical value. Furthermore, numerical simulations are carried out to illustrate our theoretical results and facilitate their interpretation

A food chain system with Holling type IV functional response and impulsive perturbations

AbstractIn this paper, a three-trophic-level food chain system with Holling type IV functional response and impulsive perturbations is established. We show that this system is uniformly bounded. Using the Floquet theory of impulsive equations and small perturbation skills, we find conditions for the local and global stabilities of the prey and top predator-free periodic solution. Moreover, we obtain sufficient conditions for the system to be permanent via the comparison theorem. We display some numerical examples to substantiate our theoretical results

Multiple attractors of host-parasitoid models with integrated pest management strategies: eradication, persistence and outbreak

Host-parasitoid models including integrated pest management (IPM) interventions with impulsive effects at both fixed and unfixed times were analyzed with regard to host-eradication, host-parasitoid persistence and host-outbreak solutions. The host-eradication periodic solution with fixed moments is globally stable if the host's intrinsic growth rate is less than the summation of the mean host-killing rate and the mean parasitization rate during the impulsive period. Solutions for all three categories can coexist, with switch-like transitions among their attractors showing that varying dosages and frequencies of insecticide applications and the numbers of parasitoids released are crucial. Periodic solutions also exist for models with unfixed moments for which the maximum amplitude of the host is less than the economic threshold. The dosages and frequencies of IPM interventions for these solutions are much reduced in comparison with the pest-eradication periodic solution. Our results, which are robust to inclusion of stochastic effects and with a wide range of parameter values, confirm that IPM is more effective than any single control tactic

Fluid Mechanics of Plankton

The cooperation between plankton biologists and fluid dynamists has enhanced our knowledge of life within the plankton communities in ponds, lakes, and seas. This book assembled contributions on plankton–flow interactions, with an emphasis on syntheses and/or predictions. However, a wide range of novel insights, reasonable scenarios, and founded critiques are also considered in this book