Integration Duration-Based Method for Unveiling Hidden Patterns of Even Number of Spirals of Chua Chaotic Attractor

Malika Belouerghi (1) , Tidjani Menacer (1) , René Lozi (2)

1 BISKRA - Université Mohamed Khider de Biskra
2 JAD - Laboratoire Jean Alexandre Dieudonné

The purpose of this article is to introduce a novel method for unveiling hidden patterns of even number of spirals in the multi-spiral Chua Chaotic attractor. This method is based on the duration of integration of this system and allows displaying every pattern containing from 1 to c+1 spirals of this attractor. After having given the equation of the multi-spiral Chua Chaotic attractor, the Menacer–Lozi–Chua (MLC) method for uncovering hidden bifurcations is explained again and a numerical example of a route of bifurcation is given. In the chosen example, the attractors found along this hidden bifurcation route display an odd number of spirals. With the novel method, during the integration process, before reaching the asymptotical attractor which possesses an odd the number of spirals, the number of spirals increases one by one until it reaches the maximum number corresponding to the value fixed by ε, unveiling both patterns of even and odd number of spirals.

Mots clés: hidden bifurcation; Chua's circuit; pattern of even number of spirals

Domaines: Systèmes dynamiques [math.DS]

Malika Belouerghi, Tidjani Menacer, René Lozi. Integration Duration-Based Method for Unveiling Hidden Patterns of Even Number of Spirals of Chua Chaotic Attractor. Indian Journal of Industrial and Applied Mathematics, 2019, 10 (1), pp.13-33. ⟨10.5958/1945-919X.2019.00020.3⟩. ⟨hal-03044722⟩