An important problem in nonlinear science is the unknown parameters estimation 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 me...

This paper is devoted to the analysis of calculation methods for solving fractional chaotic systems and impact these different approaches on behavior system. Two widely used time domain differential equations are discussed, ABM corrector-predictor method based Caputo derivative definition, long memory approach Grunwald derivative. These numerical solutions employed depict phase portrait a class...

A fuzzy observer based scheme for synchronizing two hyperchaoticoscillators via a scalar transmitted signal for cryptographic application isproposed. The Takagi-Sugeno fuzzy model exactly represents chaotic systems.Based on the general fuzzy model, the fuzzy observer of a chaotic system isdesigned on the basis of the n-shift multiple state based key encryption algorithm.The scalar transmitted s...

Due to the character of higher security of three-dimensional chaotic systems, a new algorithm based on Chen and Lorenz systems is proposed to encrypt color images. In order to increase the security of the cryptosystem, the algorithm firstly integrates image information into the Lorenz map, and then the image information is also mixed into the Chen map via the Lorenz map. Theoretical analysis an...

The main aim of this paper is to study the dynamic transitions in flows described by the two-dimensional, barotropic vorticity equation in a periodic zonal channel. In [Z.-M. Chen et al., SIAM J. Appl. Math., 64 (2003), pp. 343–368], the existence of a Hopf bifurcation in this model as the Reynolds number crosses a critical value was proven. In this paper, we extend the results in [Z.-M. Chen e...

The main aim of this research is to find an analytical and numerical study to investigate the projective Lag synchronization (PLS) of the chaotic complex nonlinear systems with uncertain parameters. We can be used this study to achieve secure communication between these systems. Based on the adaptive control technique and the Lyapunov function a scheme is designed to achieve PLS of chaotic attr...

First, this paper announces a seven-term novel 3-D chaotic system with a cubic nonlinearity and two quadratic nonlinearities. The phase portraits of the novel 3-D chaotic system are displayed and the mathematical properties are discussed. The proposed novel 3-D chaotic system has three equilibrium points, which are all unstable. We shall show that the equilibrium point at the origin is a saddle...