FITTING TRAPPING REGIONS FOR CHUA'S ATTRACTOR — A NOVEL METHOD BASED ON ISOCHRONIC LINES

Abstract

We present in this paper a novel method for fitting trapping regions for a Spiral Chua's attractor. For the values: σ0 = -0.465716…, γ0 = 0.0932544…, k = 0.3279262…, σ1 = 0.4152731…, γ1 = -0.3446764… of the parameters, the iterates of the attractor belong to two trapping regions P1 and P3 we construct with this method based uniquely on the isochronic lines. Both P1 and P3 are bounded accurately with more than 450 segments of isochronic lines. We show graphically that the inclusions π (P1) ⊂ P3, π (P3) ⊂ P1 hold. The traps for the half-Poincaré map π0 have to be constructed.