Kosambi-Cartan-Chern (KCC) Perspective on Chaos: Unveiling Hidden Attractors in Nonlinear Autonomous Systems

Abstract

This article confronts the formidable task of exploring chaos within hidden attractors in nonlinear 3-D autonomous systems, highlighting the lack of established analytical and numerical methodologies for such investigations. As the basin of attraction does not touch the unstable manifold ,there are no straightforward numerical processes to detect those attractors and one has to implement special numerical-analytical strategy.In this article we present an alternative approach that allows us to predict the basin of attraction associated with hidden attractors, overcoming the existing limitations. The method discussed here based on KCC theory (Kosambi-Cartan-Chern) which enable us to conduct a comprehensive theoretical analysis by means of evaluating geometric invariants and instability exponents, thereby delineating the regions encompassing chaotic and periodic zones. Our analytical predictions are thoroughly validated by numerical results.