Investigation of chaos in fractional order generalized hyperchaotic Henon map

Abstract

Dynamical analysis and chaos control of the fractional order generalized hyperchaotic Henon map is the main contribution of this paper. With a brief introduction to discrete fractional calculus, which is a new area of research in fractional calculus; we describe the fractional order version of generalized hyperchaotic Henon map. The classical three dimensional Henon map is represented by first order difference equations. Extending the concept of continuous time fractional calculus to discrete case, we use fractional order difference equations to describe the existing discrete chaotic maps. This gives a wide variety of chaotic patterns with variation in order of difference equations which is now a real number. The chaotic behavior of the three dimensional Henon map is ascertained by using bifurcation diagrams and chaotic attractors. Further, a control strategy is proposed to stabilize the system which will suppress chaos. The proposed control strategy is based on active control approach. The simulation results presented at the end confirms the validity of the proposed technique.