Rabinovich-Fabrikant system in view point of KCC theory in Finsler geometry

Abstract

In this paper, we geometrically investigate the Rabinovich-Fabrikant system from the view point of KCC-theory in Finsler geometry by converting first order system to second order system. The stability of system is determined by the second KCC invariant at the equilibrium points. We also show the phase portrait of deviation vector which represents the chaotic nature for a given set of parameter value and initial conditions.

Subject Classification:

• (2010) 53B40
• 53C22
• 53C60

Keywords:

• Finsler Space
• Geodesics
• KCC-theory
• Jacobi stability
• Chaos
• Rabinovich-Fabrikant system