Abstract
A new detecting method for the conditions of existence of the Hopf bifurcation is given in terms of the coefficients of the characteristic polynomial at the equilibrium by using the Hopf bifurcation theory and matrix theory. The method is available and important for the study of the existence of the Hopf bifurcation for higher differential equations which often occur in biological models, chemical models, epidemiological models, and models of AIDS.
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This research is supported by the National Science Foundation “Tian Yuan” Terms and LNM, Institute of Mathematics, the Chinese Academy of Sciences.
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Shen, J., Jing, Z. A new detecting method for conditions of existence of Hopf bifurcation. Acta Mathematicae Applicatae Sinica 11, 79–93 (1995). https://doi.org/10.1007/BF02012625
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DOI: https://doi.org/10.1007/BF02012625