Synchronization of chaos in non-identical parametrically excited systems B.A. Idowu a, * , U.E. Vincent b , A.N. Njah c a Department of Physics, Lagos State University, Ojo, Nigeria b Department of Physics, Olabisi Onabanjo University, P.M.B 2002, Ago-Iwoye, Nigeria c Department of Physics, University of Agriculture, Abeokuta, Nigeria Accepted 29 June 2007 Abstract In this paper, we investigate the synchronization of chaotic systems consisting of non-identical parametrically excited oscillators. The active control technique is employed to design control functions based on Lyapunov stability theory and Routh–Hurwitz criteria so as to achieve global chaos synchronization between a parametrically excited gyroscope and each of the parametrically excited pendulum and Duffing oscillator. Numerical simulations are implemented to ver- ify the results. Ó 2007 Elsevier Ltd. All rights reserved. 1. Introduction The nonlinear dynamics of coupled systems is of great fundamental interest because coupled systems are predom- inant in nature. Many real physical systems can be modelled by such coupled systems [1] ranging from chemical oscil- lators, population dynamics, physiological interactions, coupled neurons, to mechanical oscillators and lasers [2]. Coupled oscillators exhibit phenomenon like multistability, pattern formation, synchronization, etc. Synchronization of coupled or periodically driven complex systems has found applications in several areas of life such as circuits [3], lasers [4], plasmas [5], as well as natural systems like cardio respiratory interaction [6,7], brain activity of Parkinsonian patients [8], paddlefish electro sensitive cells [9] and solar activity [10]. Due to their importance, chaos synchronization has been studied extensively in recent times. The pioneering paper on the concept of chaos synchronization that fuelled the enormous research activities in this area was presented by Pec- ora and Carroll in 1990 [11], where they introduced a method to synchronize two identical chaotic systems evolving from different initial conditions. Thereafter, chaos synchronization has attracted the interest of many researchers due to its potential applications in various fields of science [2,11–13]. Various effective methods have been proposed to achieve chaos synchronization. These include active–passive decomposition (APD) method [2], backstepping design method [14,38], active control [15,16], invariant manifold method [17], adaptive method [18], feedback approach [18], 0960-0779/$ - see front matter Ó 2007 Elsevier Ltd. All rights reserved. doi:10.1016/j.chaos.2007.06.128 * Corresponding author. E-mail addresses: babaidowu@yahoo.com (B.A. Idowu), ue_vincent@yahoo.com (U.E. Vincent). Chaos, Solitons and Fractals 39 (2009) 2322–2331 www.elsevier.com/locate/chaos