Controlling Chaos Using Superior Feedback Technique with Applications in Discrete Traffic Models

Abstract

In recent years, discrete chaos has found a celebrated place in various dynamical phenomena of nature and science, such as population dynamics in ecology, laser technology, traffic flow system, image encryption and decryption in cryptography, secure communication, etc. But as a recent discipline, control of chaos an important field of research related to chaotic systems has come into play with many scientific and technological advances. In this article, a superior technique to control chaos in a class of one-dimensional discrete systems is developed and the unstable fixed and periodic states responsible for chaotic behavior are stabilized. Due to an extra degree of freedom of an intrinsic parameter $$\alpha$$ in superior control technique, the stability performance increases rapidly than other techniques. Further, the several theoretical as well as numerical simulation results are studied for the efficiency and effectiveness of the superior control technique followed by theorems, examples, remarks, Lyapunov exponent property, and period-doubling bifurcation representation. Moreover, using this system following discrete traffic flow problem is also discussed, “How to impart an unstable traffic behavior into stable and non-traffic zone?”.