On the Computation of Degenerate Hopf Bifurcations for n-Dimensional Multiparameter Vector Fields

The restriction of an -dimensional nonlinear parametric system on the center manifold is treated via a new proper symbolic form and analytical expressions of the involved quantities are obtained as functions of the parameters by lengthy algebraic manipulations combined with computer assisted calculations. Normal forms regarding degenerate Hopf bifurcations up to codimension 3, as well as the corresponding Lyapunov coefficients and bifurcation portraits, can be easily computed for any system under consideration.

[1]  Yongzhen Pei,et al.  Pest regulation by means of continuous and impulsive nonlinear controls , 2010, Math. Comput. Model..

[2]  Toichiro Asada,et al.  Analytical expressions of periodic disequilibrium fluctuations generated by Hopf bifurcations in economic dynamics , 2012, Appl. Math. Comput..

[3]  Kuifei Huang,et al.  Stability and Hopf bifurcation analysis of a new system , 2009 .

[4]  J. Hale,et al.  Dynamics and Bifurcations , 1991 .

[5]  S. Ruan,et al.  Bifurcations in an epidemic model with constant removal rate of the infectives , 2004 .

[6]  E. Lorenz.  Deterministic nonperiodic flow , 1963 .

[7]  Minggang Wang.  A Novel Three-dimensional Energy Resources Chaotic System with Government Regulation and Empirical Research , 2013 .

[8]  Zhipeng Qiu,et al.  Dynamics of a plant-herbivore-predator system with plant-toxicity. , 2011, Mathematical biosciences.

[9]  Y. Kuznetsov.  Elements of Applied Bifurcation Theory , 2023, Applied Mathematical Sciences.

[10]  Jiajun Lu,et al.  Stability and Hopf bifurcation for a business cycle model with expectation and delay , 2015, Commun. Nonlinear Sci. Numer. Simul..

[11]  Guanrong Chen,et al.  Local bifurcations of the Chen System , 2002, Int. J. Bifurc. Chaos.

[12]  W. Marsden.  I and J , 2012 .

[13]  Lixin Tian,et al.  Hopf Bifurcation Analysis of the Energy Resource Chaotic System , 2006 .

[14]  Yongguang Yu,et al.  Hopf bifurcation analysis of the Lü system , 2004 .

[15]  Denis de Carvalho Braga,et al.  Bifurcation analysis of the Watt governor system , 2006 .

[16]  Luis Fernando Mello,et al.  Degenerate Hopf bifurcations in the Lü system , 2009 .

[17]  Cruz Vargas de León,et al.  Stability and Hopf bifurcation in a delayed viral infection model with mitosis transmission , 2014, Appl. Math. Comput..