Delay induced dynamical behaviors in a stochastic insect outbreak model in presence of Michaelis-Menten type harvesting

Abstract

In this paper, we have considered stochastic insect outbreak model in presence of Michaelis-Menten type of harvesting. The growth of the insect species is taken as delayed logistic type together with a multiplicative noise term. The impact of internal environmental disturbances on the insect population is taken into account by adding an additive noise term in the model. The effects of the noises, cross correlation strength of the noises and time delay on the insect population are investigated and observed very rich dynamical behaviors. It is ascertained that multiplicative noise reduces population size greatly than additive noise. As usual, increase of harvesting of insect species reduces the population size at faster rate. Regime shift is possible depending on multiplicative noise only in contrast it is not possible via only additive noise. One of the key finding is the noise-delayed switching phenomenon for negatively correlated noises.

The role of harvesting in population control in the presence of correlated noise sources

“…Similarly, the mathematical model in the case of Michaelis-Menten [22] type harvesting can be written as,…”

“…The critical slowing down is closely associated to bifurcation points and at a bifurcation point, the potential has flat bottom. The deterministic bifurcation curve of the population can be obtained by putting σ = 0 and D = 0 in the equation ( 21) and (22). It can be noticed from figures 10(a) and 11(a) that the deterministic counterpart of the stochastic models (4) and (5) i.e, model (2) and (3) are bistable in biological sense.…”

“…There are various types of harvesting strategies eg. constant rate of harvesting [21], Michaelis-Menten type harvesting [22], density dependent harvesting [23], quadratic harvesting [24], etc., in theoretical ecology.…”

The Role of Harvesting in Population Control in Presence of Multiple Stochastic Noise Sources

“…where α is half-saturation level for predation, β is the predation rate and ρ c is the constant absolute rate of harvesting. Similarly, the mathematical model in the case of Michaelis-Menten [29] type harvesting can be written as,…”

“…There are various types of harvesting strategies eg. constant rate of harvesting [28], Michaelis-Menten type harvesting [29], density dependent harvesting [30], quadratic harvesting [31], etc. in theoretical ecology.…”