Novel Single Bounded Input Control Synchronization Criterion for a Category of Hyperchaotic and Chaotic Systems in Presence of Uncertainties

Dynamical systems that have a chaotic underlying structure have a sensitive dependency on the initial conditions and the values of their parameters. In this piece of work, a straightforward method for solving the synchronization issue in master-slave arrangement for a category of chaotic or hyperchaotic systems, in which perturbations are present in the parameters of the response system, is discussed. The desired control signal is bounded by the initial state when the controller is activated. There is just one control input that is used, and it is derived from Lyapunov's concept of stability. In general, it is tricky to synchronize hyperchaotic or chaotic systems with single controller, and the work turns out to be significantly more complex when the parameters of the slave system are perturbed. The feedback controller using single input that has been constructed makes certain that the state variables of the response system are in synchronization with the state variables that correspond to them in the drive system. In order to attain the desired level of synchronization, the required conditions that must be satisfied to do so have been identified utilizing Lyapunov's stability analysis in a simple manner. In addition, numerical illustrations have been provided in order to support and confirm the theoretical findings of the paper.