Bursting mechanism in a memristive Lorenz based system and function projective synchronization in its-fractional-order form: Digital implementation under ATmega328P microcontroller

Abstract In this paper, bifurcation mechanism of bursting oscillations and function projective synchronization of the fractional order form for a memristive Lorenz based system are investigated. One of the key results is the dependance of relaxation time of bursting oscillation on the fractional order derivative. The newly proposed system has a line equilibrium and accordingly, features hidden attractors. When the system is divided into two subsystems labeled slow subsystem(SS) and fast subsystem(FS), stability analysis indicates that bursting oscillations result from the switching of the equilibrium point of the(FS) between stable and unstable states. We refer this class of bursting as ”source/bursting”. The second aspect of this paper deals with the study of fractional order of the system precisely function projective synchronization in a relay topology. By using some standard nonlinear diagnostic tools such as bifurcation diagram, largest Lyapunov exponent, phase space trajectory and power spectrum, the study of the fractional model reveals that the dynamics strongly depends on system parameters , fractional order q as well as on initial conditions. With a set of chosen parameters , the proposed scheme achieves function projective synchronization in a finite time despite the unpredictability of the scaling function. The Results of digital implementation based on a ATmega328P microcontroller are in good agreement with those found by numerical simulations.