In this research, an integrated pest management model using impulsive differential equations has been investigated for Jatropha curcas plantation to control its natural pests through relying on the release of infective pest individuals and spraying of chemical pesticides. First, identify susceptible pest eradication solutions and assess their feasibility. We then show that all system variables are bounded. Using Floquet's theory and the small amplitude perturbation method, it is obtained that there exists an asymptotically stable susceptible pest eradication periodic solution when the release amount of infected pest is larger than the critical maximum value (or strength of chemical pesticide spraying is larger than some critical maximum value). Also, we have established the permanence of the system. After comparison, it is explored that integrated pest management is more effective than biological control or chemical control. Finally, verify the analytical results through numerical simulation.
This paper mainly focuses on the velocity-constrained consensus problem of discrete-time heterogeneous multi-agent systems with nonconvex constraints and arbitrarily switching topologies, where each agent has first-order or second-order dynamics. To solve this problem, a distributed algorithm is proposed based on a contraction operator. By employing the properties of the stochastic matrix, it is shown that all agents' position states could converge to a common point and second-order agents' velocity states could remain in corresponding nonconvex constraint sets and converge to zero as long as the joint communication topology has one directed spanning tree. Finally, the numerical simulation results are provided to verify the effectiveness of the proposed algorithms. INDEX TERMS Heterogeneous, multi-agent systems, nonconvex constraint, consensus.
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