A novel approach to obtain analytical-numerical solutions of nonlinear Lorenz system

作者：Gonzalez Parra Gilberto^*; Acedo Luis; Arenas Abraham J

来源：Numerical Algorithms, 2014, 67(1): 93-107.

DOI：10.1007/s11075-013-9776-x

• Modal series
• Lorenz system
• Nonlinear dynamical system
• Global analytical solution

In this research we apply an analytic approach to solve the well-known Lorenz system in the non-chaotic regime. The proposed approach is based on modal expansion by infinite series. The analytical-numerical results show that for real initial conditions and under the non-convective regime the modal expansion series reproduce correctly the dynamical behavior of the solution of the Lorenz system. The validity and reliability of the proposed analytical approach with few terms is tested by its application to the convective and non-convective regime with various parameter values. The main advantage is that the obtained solution is global and is presented in analytical form.

• 出版日期2014-9