Dynamical Properties of a Modified Chaotic Colpitts Oscillator with Logarithmic Function

In this paper, two logarithmic non-linearities are proposed for a new four-dimensional chaotic system. The phase portrait, Lyapunov exponent, bifurcation, stability, and other dynamical features of the new chaotic system are all discussed. The multi-stability of the new chaotic system with coexisting attractors has been established. The adaptive backstepping control approach with proper Lyapunov functions is used in the control application to retrieve the unknown parameters of the system. To synchronise the states between the drive-response system, non-linear feedback control is used, as well as backstepping control to synchronise the states on the system's error dynamics. Op-amp circuits are used to create the electronic circuit design for a new chaotic system. The system's efficiency is confirmed using MATLAB numerical simulation.