1. Suppose a population is growing in an environment with a carrying-capacity of 100 and ascarcity-constant of 20. Suppose further that the rate of change of the population would beproportional to the population by a factor of 0.01 were it not for these environmentalconstraints. Set up a differential equation modelling the population then draw a phase linenext to several specific solutions of the differential equation. Indicate whether the equilibriumsolutions are sinks, sources, or nodes.

As per the question, we will examine a population model subject to environmental constraints, such…

Answered: Suppose a population is growing in an…

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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Can you find all equilibria of each system of differential equations and use the analytical approach to determine the stability of each equilibrium? dx1/dt= 4x1(1-x1)-2x1x2 dx2/dt= x2(2-x2)-x2
Consider a time-varying population that follows the logistic population model. The population has a limiting population of 800, and at time t = 0, its population of 200 is growing at a rate of 60 per year. Please write a differential equation for the populatoin P(t) that models this scenario.
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38. Given the power regression model y = 40x^1.3, which is the linear regression model after transforming to a log-log graph? Y = 1.3X + 1.60 Y = 0.20X + 0.11 Y = 0.20X + 0.36 Y = 1.60X + 0.11
Disease epidemics can be modelled by differential equations. Suppose we have two sub-populations of individuals in a city: individuals who are infected with some virus (I) and individuals who are susceptible to infection (S). We assume that if a susceptible person interacts with an infected person, there is a probability p that the susceptible person will become infected. Each infected person recovers from the infection at a rate r and becomes susceptible again. The differential equations that model these population sizes are TI - PSI, dS dt dI dt pSI - TI. (a) Assuming no one dies from the virus, the total population N is a constant number defined as N = S+I. Show in this case that you can reduce the above system to the single differential equation for I. (b) Find the general solution I(t) to the ODE found in part (a). (c) If I (0) = Io, give the equation for the unknown constant in terms of Io, N, p and r.
Consider the DEdy/dt = y^(3)*(y −1)2(y + 2).Draw the phase line and a graph showing the long-term behavior of solutions.

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