Optik 127 (2016) 9532–9537 Contents lists available at ScienceDirect Optik j o ur nal ho me pa ge: www.elsevier.de/ijleo Short note Predictive synchronization of chaotic and hyperchaotic energy resource systems Imen Benchabane, Abdelkrim Boukabou ∗ Department of Electronics, Jijel University, Ouled Aissa, Jijel 18000, Algeria a r t i c l e i n f o Article history: Received 10 March 2016 Accepted 3 May 2016 Keywords: Energy resource system Chaotic and hyperchaotic behaviors Predictive synchronization a b s t r a c t The problem of chaos synchronization for energy resource system is investigated. In this paper, a simple stability criterium for both chaotic and hyperchaotic energy resource sys- tems is obtained. A unified prediction-based control strategy is designed to make these systems synchronized. Numerical simulations verify the effectiveness of our methodology. © 2016 Published by Elsevier GmbH. 1. Introduction Synchronization of real world chaos-based systems has become a new and important area of research [1]. Since the idea of synchronizing chaotic systems has been introduced by Pecora and Carroll in 1990 [2], many authors developed different methods to solve this problem. More recently, predictive synchronization of chaotic satellite systems and hyperchaotic systems were investigated in [3,4]. Sun et al. [5,6] proposed new chaotic and hyperchaotic systems to analyze the energy resource demand-supply in some regions of China. Synchronization has been achieved using adaptive control [7] and linear control [8,9]. The aim of this paper is to apply prediction-based control to synchronize both chaotic and hyperchaotic energy resource systems. This paper is organized as follows: In Section 2 we apply predictive synchronization to chaotic energy resource system and numerical results are given to show this process. In Section 3 we perform predictive synchronization on hyperchaotic energy resource system and numerical simulations are provided. Finally, conclusion is given in Section 4. 2. Predictive synchronization of chaotic energy system The three-dimensional (3-D) energy resource system [5] is expressed by the following set of ordinary differential equa- tions ˙ x = a 1 x(1 - x/M) - a 2 (y + z) ˙ y = -b 1 y - b 2 z + b 3 x[N - (x - z)] ˙ z = c 1 z(c 2 x - c 3 ) (1) ∗ Corresponding author. E-mail address: aboukabou@univ-jijel.dz (A. Boukabou). http://dx.doi.org/10.1016/j.ijleo.2016.05.005 0030-4026/© 2016 Published by Elsevier GmbH.