On controlling chaos in discrete dynamical systems via a two-step feedback algorithm with applications

Chaos theory is based on the fact that how small initial changes may lead to large unpredictable changes in the final outcome. Controlling chaos in nonlinear dynamical systems by stabilising their fixed and periodic states using different feedback algorithms has found potential applications in several working areas like traffic control, reduction control, heat convection, cardiac arrhythmia, chemical chaos, spine-wave instability. This article deals with a chaos controlling mechanism driven by Thianwan's feedback algorithm. Initially, the controlling mechanism is defined and a few stability theorems deciding the effective ranges of the control parameters are proved with some examples of discrete systems. The results are supported by analytical study and numerical simulations. The efficacy of the stability intervals determined for the fixed and periodic states in the controlling mechanism is illustrated by using the Lyapunov property. Finally, an improved control-based traffic flow model is provided as an application of the proposed controlling mechanism.