Numerical Simulation of a Class of Hyperchaotic System Using Barycentric Lagrange Interpolation Collocation Method

Abstract

Hyperchaotic system, as an important topic, has become an active research subject in nonlinear science. Over the past two decades, hyperchaotic system between nonlinear systems has been extensively studied. Although many kinds of numerical methods of the system have been announced, simple and efficient methods have always been the direction that scholars strive to pursue. Based on this problem, this paper introduces another novel numerical method to solve a class of hyperchaotic system. Barycentric Lagrange interpolation collocation method is given and illustrated with hyperchaotic system (x˙=ax+dz-yz,y˙=xz-by, 0≤t≤T,z˙=cx-z+xy,w˙=cy-w+xz,) as examples. Numerical simulations are used to verify the effectiveness of the present method.

Numerical solution of a class of advection-reaction-diffusion system

“…In this paper, we use displacement method to impose the initial boundary conditions. The detailed procedure see [8][9][10]. In calculation, we choose the chebyshev nodes.…”

“…These methods include B-spline method [1,2] the variational iteration method [3], homotopy perturbation method [4], integral transform [5], and so on [6,7]. The barycentric interpolation collocation method [8][9][10][11][12][13] is a high precision method. In this paper, we mainly employ the barycentric Lagrange barycentric interpolation collocation method to solve the systems (1).…”

Numerical Solution of a Class of Predator-Prey Systems with Complex Dynamics Characters Based on a Sinc Function Interpolation Collocation Method

“…In general, the exact solution of system (4) cannot be obtained, and the approximate solution must be obtained by numerical calculation. Although many kinds of numerical methods of the nonlinear reaction-diffusion system have been announced, such as finite difference method [14], B-spline method [15], finite element method [16,17], spectral method [18][19][20], the perturbation method and variational iteration method [21,22], barycentric interpolation collocation method [23][24][25][26], and reproducing kernel method [27,28], this paper investigates some nonlinear diffusion predator-prey systems [5,12,13] based on a new interpolation collocation method, and the model (21) is adopted as an example to elucidate the solution process.…”

Numerical Simulation of the Lorenz-Type Chaotic System Using Barycentric Lagrange Interpolation Collocation Method

“…With the development of numerical analysis, there are some high-precision methods, such as variational iteration method [11][12][13], BLICM [14][15][16][17][18][19][20][21][22], and so on [23]. J.P. Berrut [24][25][26] introduced barycentric Lagrange interpolation, [27,28] studied numerical stability of barycentric Lagrange interpolation, and [15,16] give algorithm of BLICM.…”

“…J.P. Berrut [24][25][26] introduced barycentric Lagrange interpolation, [27,28] studied numerical stability of barycentric Lagrange interpolation, and [15,16] give algorithm of BLICM. Some authors [14,[17][18][19][20][21][22] have used BLICM to solve all sorts of problems and show the BLICM is a high precision numerical method. This paper suggests the BLICM to solve the Lorenz system.…”