Multistability and period-adding in a logarithmic Lorenz system

Abstract

In this paper, we design and explore a novel 3D autonomous nonlinear system with logarithmic nonlinearity. It is framed from the Lorenz model by replacing the variable [Formula: see text] in the second equation by the nonlinear logarithmic term [Formula: see text]. The bi-parametric dynamics of the modeled system is presented. Studies reveal the emergence of shrimp-shaped periodic structures in chaotic regime with period-adding phenomenon, and coexisting periodic-chaotic attractors, which do not occur in the Lorenz model. The stability, bifurcation patterns, and chaotic behaviors of the system are explored with the aid of bifurcation diagrams, phase portraits and Lyapunov exponents. The complexity of the basin sets for the coexisting attractors is also studied.