Optimal phase control in a Remoissenet–Peyrard substrate potential: numerical and analogical investigations

This paper addresses the numerical and analogical investigations on the optimal phase control in a system with Remoissenet–Peyrard substrate potential. To achieve our objectives, some numerical and analogical tools such as the two dimensions largest Lyapunov exponents, bifurcation diagrams, isospike diagrams and the PSpice software have been used. Numerical results showed that when a weak perturbation parameter is applied to the elastic and friction terms of the equation describing the motion of the system, its behavior can be controlled from a chaotic dynamic to a periodic one. Furthermore, when the perturbations are applied to the elastic parameter, the system presents less chaotic dynamics than in the case where they are applied to the friction parameter. The analogical results obtained after implementing the system using electronic laws confirmed the stick–slip phenomenon early found in the system and proved the efficiency of the control strategy.