Limit cycle and bifurcation of nonlinear problems

By Ji-Huan He. 2005

338 citations recorded by the source corpus.

In this paper a simple but effective iteration method is proposed to search for limit cycles or bifurcation curves of nonlinear equations. Some examples are given to illustrate its convenience and effectiveness.

Subfields: Geometry and Topology, Modeling and Simulation, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/807cec3a864affc3adff0ce1c8702b3ade6df277

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In Geometry and Topology

In Modeling and Simulation

In Statistical and Nonlinear Physics

Citations in the corpus

Application of He's Homotopy Perturbation Method to Sumudu Transform (2007, methodology): “This new method was further developed and improved by He and applied to non-linear oscillators with discontinuity [7], asymptotology [8], non-linear wave equations [9], bifurcation of nonlinear problems [10], limit cycle [11], delaydifferential equations [[12], and boundary values problems [13].”
On The Exact Solution of Newell-Whitehead-Segel Equation Using the Homotopy Perturbation Method (2011, methodology): “The Idea Of Homotopy Perturbation Method: The homotopy perturbation method (HPM) is originally initiated by (He, 1999; He, 2005; Yildirim, 2009; He, 2006; He, 2006; He, 2006; He, 2005; He, 1998; He, 1998; He, 1999; He, 1999; He, 2000; He, 2006; He, 2005; He, 2005; He, 2005; Koçak et al., 2011).”
Explicit analytical solutions of the generalized Burger and Burger–Fisher equations by homotopy perturbation method (2009, methodology): “This method was further developed and improved by He and applied to nonlinear oscillators with discontinuities [12], nonlinear wave equations [13], asymptotology [14], boundary value problem [15], limit cycle and bifurcation of nonlinear problems [16] and many other subjects.”
A new domain decomposition algorithm for generalized Burger’s–Huxley equation based on Chebyshev polynomials and preconditioning (2009, methodology): “Recently various powerful mathematical methods such as homotopy perturbation method [6–8], variational iteration method [9–18], Exp-function method [19,20], F-expansion method [21], and others [22,23] have been proposed to obtain exact and approximate analytic solutions for nonlinear problems in par”