Exponential synchronization of a new Lorenz-like attractor with uncertain parameters via single input

The new Lorenz-like attractor, reported by Li et al. (2009) [1], includes a product term of system parameters. It can be predicted that chaotic synchronization of this new chaotic system becomes more complicated by taking account of uncertain system parameters. In this paper, the exponential synchronization between two nearly identical Lorenz-like attractors by applying single input controller associated with system parameter update laws is proposed. Unlike multiple control inputs and state variable feedbacks required in chaotic synchronization in the literature, the proposed single input controller includes only one state variable proportional feedback. Two kinds of system parameter update laws are introduced and sufficient conditions are provided to guarantee exponential stability of both synchronous errors and system parameter errors. In addition, numerical simulations are also performed to verify the effectiveness of presented schemes.