On the global dynamics of a three-dimensional forced-damped differential system

Abstract

In this paper by using the Poincaré compactification of ℝ³ we make a global analysis of the model xʹ = ax + y + yz, yʹ = x – ay + bxz, zʹ = cz – bxy. In particular we give the complete description of its dynamics on the infinity sphere. For a + c = 0 or b = 1 this system has invariants. For these values of the parameters we provide the global phase portrait of the system in the Poincaré ball. We also describe the α and ω-limit sets of its orbits in the Poincaré ball.

Keywords:

• Global dynamics
• Poincaré compactification
• forced-damped system
• invariant algebraic curve
• invariant

2000 Mathematics Subject Classification:

• 34C05
• 34C07
• 34C08