1. Consider the following nonlinear system of differential equations(competing

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1. Consider the following nonlinear system of differential equations(competing species): x'=x(3−x− 2y) y'=y(2− x−y) a) Find all equilibrium points. b) Solve the linearized systems about these equilibrium points. c) Contruct a phase portrait for this system. d) Consider the initial populations are at x(0) = 1 and y(0) = 2. Describe the long term behavior of these populations. 1. Consider the following nonlinear system of differential equations(competing species): x'=x(3−x− 2y) y'=y(2− x−y) a) Find all equilibrium points. b) Solve the linearized systems about these equilibrium points. c) Contruct a phase portrait for this system. d) Consider the initial populations are at x(0) = 1 and y(0) = 2. Describe the long term behavior of these populations.

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