Research Information System
Istanbul Nonlinear Dynamics & Integrability Workshop 2025, İstanbul, Turkey, 31 October 2025, pp.0-1, (Summary Text)
This study presents a comprehensive framework examining the role of fixed point iteration theory in the analysis and control of chaotic behaviors in nonlinear discrete dynamical systems. To achieve chaos suppression, various iterative control mechanisms, such as Mann, Ishikawa, Noor, Multistep, S, Picard-S, Thakur, Karakaya, Normal-S, M and multivalued fixed point iterations are theoretically formulated, and their stability conditions are analytically established. By employing Gâteaux and Fréchet derivatives in Banach spaces, derivative-based control intervals are derived to identify stability and instability regions depending on system parameters, with the validity of these regions verified through Lyapunov exponent computations. Extending beyond classical single-valued models, one-step feedback mechanisms for multivalued discrete dynamical systems are proposed, and their stabilizing effects under contraction conditions are investigated. Computer simulations performed on logistic and tent-type chaotic maps confirm that the proposed iterative control mechanisms transform chaotic trajectories into stable regimes. Furthermore, applications to tent-based electronic circuit models and the traffic control model demonstrate the effectiveness of the developed methods in both engineering and system dynamics contexts. Collectively, this work bridges the theoretical gap between abstract fixed point theory and practical chaos control, offering an integrated framework that connects mathematical analysis with real-world engineering implementations.