A Locust Phase Change Model with Multiple Switching States and Random Perturbation

Abstract

Insects such as locusts and some moths can transform from a solitarious phase when they remain in loose populations and a gregarious phase, when they may swarm. Therefore, the key to effective management of outbreaks of species such as the desert locust Schistocercagregaria is early detection of when they are in the threshold state between the two phases, followed by timely control of their hopper stages before they fledge because the control of flying adult swarms is costly and often ineffective. Definitions of gregarization thresholds should assist preventive control measures and avoid treatment of areas that might not lead to gregarization. In order to better understand the effects of the threshold density which represents the gregarization threshold on the outbreak of a locust population, we developed a model of a discrete switching system. The proposed model allows us to address: (1) How frequently switching occurs from solitarious to gregarious phases and vice versa; (2) When do stable switching transients occur, the existence of which indicate that solutions with larger amplitudes can switch to a stable attractor with a value less than the switching threshold density?; and (3) How does random perturbation influence the switching pattern? Our results show that both subsystems have refuge equilibrium points, outbreak equilibrium points and bistable equilibria. Further, the outbreak equilibrium points and bistable equilibria can coexist for a wide range of parameters and can switch from one to another. This type of switching is sensitive to the intrinsic growth rate and the initial values of the locust population, and may result in locust population outbreaks and phase switching once a small perturbation occurs. Moreover, the simulation results indicate that the switching transient patterns become identical after some generations, suggesting that the * Author for correspondence evolving process of the perturbation system is not related to the initial value after some fixed number of generations for the same stochastic processes. However, the switching frequency and outbreak patterns can be significantly affected by the intensity of noise and the intrinsic growth rate of the locust population.

Application of Remote Sensing Data for Locust Research and Management—A Review

“…Furthermore, locust population dynamics are also influenced by land management [ 7 ]. For locust phase polyphenism and population density research, we refer the reader to [ 8 , 9 , 10 , 11 ].…”

KCC Analysis of a One-Dimensional System During Catastrophic Shift of the Hill Function: Douglas Tensor in the Nonequilibrium Region

“…It is well known that although nonlinear systems (e.g., ecosystems) may experience gradual changes (e.g., temperature change), this can be punctuated by a sudden drastic shift to a contrasting state (e.g., a drastic change in a population) ( [May, 1977;Van Nes & Scheffer, 2007;Xiang et al, 2016]). In previous studies ([Scheffer et al, 2001;Kéfi et al, 2013;Donangelo et al, 2010]), this jump phenomenon (bifurcation) is referred to as a catastrophic shift; thus, we use this term in the present paper.…”

A Holling Type II Discrete Switching Host-Parasitoid System with a Nonlinear Threshold Policy for Integrated Pest Management

“…Such systems, based on the ordinary differential equation (ODE) model for the predator-prey interaction, have been investigated in recent publications (see [12,13,[16][17][18] for relevant references). In addition, Xiang and his co-authors [19][20][21][22][23][24] discussed the complex dynamic behaviour of discrete switching systems. However, in the above publications, the authors only considered the relationship between ET and the density of a pest population in generation t, that is, the threshold condition is linear or the switching surface is a straight line.…”