Q4Suppose that the density N₁ in year t of a beetle population is described bythe following discrete-time Hassell model with explicit delay:RNt(1+ №₁-T)²where R> 0 and the delay T is a non-negative integer.Nt+1 =By using the Stability Triangle or otherwise, show that in the case T = 1 if R is increasedfrom 1, the equilibrium is first monotonically stable, then oscillating stable and finallyoscillating unstable, and identify the corresponding critical values of the parameter R atwhich the behaviour changes.

As per the question we are given a discrete dynamic system and we have to describe the behaviour of…

Answered: Q4 Suppose that the density N₁ in yeart…

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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b) The random variable X, has probahility density function (nents 1>0 fa(2) = otherwise Using the moment generating functions, show that (i) X, has a limiting distribution which is degenerate at x = 8 (ii) Z, = n(X, - 8) has a limiting distribution which is exponential with mean 1. %3!
For an M/M/1 queueing system, L =λ/(μ - l). Suppose that λ and μ are both doubled. How does L change? How does W change? How does WQ change?How does LQ change? (Remember the basic queueing relationships, including Little’s formula.)
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Suppose that a constant voltage source of 10 V supplies a current I (in mA) through a resistive load with a stochastic resistance R. (in k) defined by the PDF as follows. fR (r) B = = C = -{1 1500r750r²- 742.5, 0.9≤r≤1.1 elsewhere Knowing from ohm's law that I = Ꭱ the following PDF: fi(i) = { ¦ (Ai + Bi² + C), A = 0₂ and I the derived distribution of I is given by 100 11
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