Journal de théorie et applications du mensonge généralisé

Spruce Budworm Model With and Without Delay

Abstract

Dipak Maji

Mathematical modeling is the art of translating problems from an application area into tractable mathematical formulations whose theoretical and numerical analysis provides insight, answers, and guidance useful for the originating application.

Mathematical modeling:

• is indispensable in many applications

• gives direction for the problem solutions

• prepares the way for better designing or control system

Learning about mathematical modeling is an important step for a theoretical mathematical training to an application oriented mathematical expertise, and makes the student fit for mustering the challenges of our modern technological culture. One of the most important mathematical model is Spruce Budworm model for researchers as well as for students. Understanding the dynamic of spruce budworm is very important for the protection of spruce and fir trees of Canada and Northern Minnesota (also in recent time Indian Himalayan range forest). This model was designed to identify the (a) critical factors that affect the Budworm population dynamics (b) to evaluate the effect of budworm population on the growth and yield of wood industry and also the present loss claimed by irruptions done by Budworm (c) to formulate mathematical model and to find out the steady state and the existence of the steady state and steady state analysis. The bifurcation analysis and the hysteresis effect of the model has been discussed. Analysis of the equilibrium stability and examination of amplitudes and periodic oscillations are conducted, and the effect of Budworm control, immature population control and predation by the birds are assessed.