Homoclinic and heteroclinic solutions of cubic strongly nonlinear autonomous oscillators by hyperbol

• 作 者: SZE Kam Yim
• 机 构: Department of Mechanical Engineering,The University of Hong Kong,
• 出 处: Science China(Technological Sciences)
• 发表日期: 2010年03期
• 关键词: hyperbolic cubic oscillator autonomous illustrate perturbation Kutta Runge latte

The hyperbolic Lindstedt-Poincaré method is applied to determine the homoclinic and heteroclinic solutions of cubic strongly nonlinear oscillators of the form x + c1 x + c3 x 3= ε f (μ,x,x).In the method,the hyperbolic functions are employed instead of the periodic functions in the Lindstedt-Poincaré procedure.Critical value of parameter μ under which there exists homoclinic or heteroclinic orbit can be determined by the perturbation procedure.Typical applications are studied in detail.To illustrate the accuracy of the present method,its predictions are compared with those of Runge-Kutta method.

The hyperbolic Lindstedt-Poincaré method is applied to determine the homoclinic and heteroclinic solutions of cubic strong nonlinear oscillators of the form x + c1 x + c3 x 3 = ε f (μ, x, x) .In the method, the hyperbolic functions are employed instead of the periodic functions in the Lindstedt-Poincaré procedure. Critical value of parameter μ under which there exists homoclinic or heteroclinic orbit can be determined by the perturbation procedure. Typical applications are studied in detail. To illustrate the accuracy of the present method, its predictions are compared with those of Runge-Kutta method.