An important problem in nonlinear science is estimation of unknown parameters in Loranz Chaotic System. Clearly, the parameter estimation for Chaotic Systems is a multidimensional continuous optimization problem, where the optimization goal is to minimize mean squared errors (MSEs) between real and estimated responses for a number of given samples. The Bees algorithm (BA) is a new member of meta-heuristics. BA tries to model natural behavior of honey bees in food foraging. This paper focuses on using the BA to solve this problem. Simulation results demonstrate the merit, effectiveness and robustness of BA.

Project scheduling in the resource-constrained situation is one of the key issues of project-oriented organizations. The aim of Resource-Constrained Project Scheduling Problem (RCPSP) is to  nd a schedule with minimum makespan by considering precedence and resource constraints. RCPSP is a combinatorial optimization problem and belongs to the NP-hard class of problems. The exact methods search the entire search space and are unable to solve a large-sized project network problem. Thus, metaheuristics are used to solve this problem in a short computational time. Due to the probabilistic nature of metaheuristics, it is a challenging problem to make a balance between exploitation and exploration phases. The literature review shows that embedding of chaos improves both the convergence speed and the local optima avoidance of metaheuristics. This paper presents a Chaotic Vibrating Particles System (CVPS) optimization algorithm for solving the RCPSP. Vibrating Particles System (VPS) is a physics-inspired metaheuristic which mimics the free vibration of single-degree-of-freedom Systems with viscous damping. The performance and applicability of the CVPS are compared with the standard VPS and  ve well-known algorithms on three benchmark instances of the RCPSPs. Experimental studies reveal that the proposed optimization method is a promising alternative to assist project managers in dealing with RCPSP.

In this article, Synchronization and control methods are discussed as essential topics in science. The contraction method is an exciting method that has been studied for the synchronization of Chaotic Systems with known and unknown parameters. The controller and the dynamic parameter estimation are obtained using the contraction theory to prove the stability of the synchronization error and the low parameter estimation. The control scheme does not employ the Lyapunov method. For demonstrate the ability of the proposed method, we performed a numerical simulation and compared the result with the previous literature.

This paper addresses a nonlinear observer based control scheme to synchronize Chaotic Systems subject to uncertainties and external disturbances. It is assumed that the dynamic of slave System is not completely known. In order to compensate for the System perturbation resulting from parameter variations and mismodeling phenomena, an adaptive neural network observer is employed to handle this problem. A nonlinear observer for a class of nonlinear Systems is proposed based on a generalized dynamic recurrent neural network. The weights of the proposed neural network in the observer are tuned on-line with no off-line learning phase required. Also, no exact information of the nonlinear term of the System is required and this important characteristic compensates considerable part of uncertainty. To realize control purpose, two controllers are considered. At first, PID controller is combined with proposed observer and then 2nd order sliding mode controller called twisting algorithm is applied to synchronize Systems. This method is implemented on the Duffing Chaotic Systems and simulation results confirm the effectiveness of the proposed method.