Complex dynamics and coexistence of period-doubling and period-halving bifurcations in an integrated pest management model with nonlinear impulsive control

Abstract

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.

Dynamical Behavior of a Predator‐Prey System Incorporating a Prey Refuge with Impulse Effect

“…With profound understanding of human nature, the theory of impulsive differential equations [22][23][24] becomes more perfect. e impulsive differential equation has become a widely concerned subject in recent years, and it is more appropriate to apply to biological systems for the actual reality, for example [25][26][27][28][29][30][31][32][33][34][35].…”

Farming awareness based optimum interventions for crop pest control

“…The nondegradable chemical residues, which construct to damaging stages, are the core cause of health and environmental hazards and most of the present hostility toward them. The imperative role of microbial pesticides in integrated pest management, is well-known in agriculture, forestry, and public fitness [4,5,6]. As included pest administration, biological pesticides give noticeable pest control reliability in the case of plants [7].…”

Dynamics behaviors of a stage‐structured pest management model with time delay and impulsive effects

“…In the past few years, some biocontrol models on pest management described by impulsive differential equations have been widely studied by the researchers (see previous studies [1][2][3][4][5][6][7][8] ). In Zhang et al, 1 a pest management model with periodic pesticide input was considered, and some sufficient conditions for both global attractivity of the periodic solution and the permanence were derived.…”