Consider the nonlinear two dimensional Lotka- Volterra system r(t) = r(t)-x2(t)-Aix(t)y(t), y(t) = y(t)-y2(t)-Apr(t)y(t), with the constants λ| > 1 and λ2 > 1, and we are interested in solutions of (3) that satisfy (0) 0, and y(0)0 Use the Poincaré-Bendixson and Bendixson-Dulac theorems to show that all trajec- tories of the system (3) tend to (1,0) or (0, 1), depending on the initial conditions (To: o).

Consider the nonlinear two dimensional Lotka- Volterra system r(t) = r(t)-x2(t)-Aix(t)y(t), y(t) = y(t)-y2(t)-Apr(t)y(t), with the constants λ| > 1 and λ2 > 1, and we are interested in solutions of (3) that satisfy (0) 0, and y(0)0 Use the Poincaré-Bendixson and Bendixson-Dulac theorems to show that all trajec- tories of the system (3) tend to (1,0) or (0, 1), depending on the initial conditions (To: o).

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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