In a pond, green sunfish competes with bluegill for food. Let x, y be the amount of green sunfish and bluegill respectively (in thousands). Suppose that the interaction of the green sunfish and the bluegill is described by the system x' = 3x – x2 (1) (2) xy, y' = 3y – 2y – 0.5xy • Find all critical points of this system. • Compute Jacobian matrices of the system at the critical points; determine types of these points if possible (saddle, nodal source/sink, spiral source/sink). Sketch the phase portrait of the (nonlinear) system in the domain a > 0, y > 0 (cv. examples 3,4 in Sec. 6.3).

In a pond, green sunfish competes with bluegill for food. Let x, y be the amount of green sunfish and bluegill respectively (in thousands). Suppose that the interaction of the green sunfish and the bluegill is described by the system x' = 3x – x2 (1) (2) xy, y' = 3y – 2y – 0.5xy • Find all critical points of this system. • Compute Jacobian matrices of the system at the critical points; determine types of these points if possible (saddle, nodal source/sink, spiral source/sink). Sketch the phase portrait of the (nonlinear) system in the domain a > 0, y > 0 (cv. examples 3,4 in Sec. 6.3).

Linear Algebra: A Modern Introduction

4th Edition

ISBN:9781285463247

Author:David Poole

Publisher:David Poole

Chapter3: Matrices

Section3.1: Matrix Operations

Problem 20EQ: Referring to Exercise 19, suppose that the unit cost of distributing the products to stores is the...

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