Detection of Generalized Synchronization in Chaotic Oscillators Using Multiobjective System Identification

This work investigates the detection of generalized synchronization between chaotic oscillators, specifically a Rössler system (master) and a Lorenz system (slave), coupled unidirectionally. The study explores how the location of fixed points, the Lyapunov exponent, and the observability of the coupling signal influence the occurrence of generalized synchronization. To detect generalized synchronization, multiobjective system identification techniques and polynomial NARX models were employed to derive a mathematical function capable of describing the relationship between the coupled states. Results demonstrate that the observability of the coupling signal plays a crucial role in generalized synchronization, proving to be significantly more influential than the coupling factor. To my knowledge, this is the first work to successfully employ multiobjective system identification tools for the detection of generalized synchronization. The main contribution of this work is the successful application of this innovative approach, which derived models capable of confirming generalized synchronization under specific coupling conditions. This result highlights the importance of analyzing the dynamics of the coupled system, using fixed points and Lyapunov exponents as reliable indicators of generalized synchronization.