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9 September 2019 Study on the Influence of Stochastic Parameters of HOPF Bifurcation System in Coastal Management
Ying Qiao, Yuansheng Huang, Jimin Li
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Abstract

Qiao, Y.; Huang, Y.-S., and Li, J.-M., 2019. Study on the influence of stochastic parameters of HOPF bifurcation system in coastal management. In: Gong, D.; Zhu, H., and Liu, R. (eds.), Selected Topics in Coastal Research: Engineering, Industry, Economy, and Sustainable Development. Journal of Coastal Research, Special Issue No. 94, pp. 696–700. Coconut Creek (Florida), ISSN 0749-0208.

Shallow water bathymetric data is an important foundation for scientific research and coastal management.HOPF bifurcation, as a complex nonlinear phenomenon, has been widely studied in ocean and other scientific and technological fields.In this paper, the HOPF bifurcation of stochastic Lorenz-family systems with random parameter is addressed. In the analysis, the stochastic Lorenz-family system is firstly transformed into an equivalent deterministic system by the Chebyshev polynomial approximation, so that the HOPF bifurcation of stochastic system can be reduced into that of the equivalent deterministic system. Combined with the definition of HOPF bifurcation and some mathematical analysis tools, the critical value of HOPF bifurcation is obtained and the influence of the random parameter on HOPF bifurcation in stochastic Lorenz-family system is analyzed. Atlast these results are verified by numerical simulation.

©Coastal Education and Research Foundation, Inc. 2019
Ying Qiao, Yuansheng Huang, and Jimin Li "Study on the Influence of Stochastic Parameters of HOPF Bifurcation System in Coastal Management," Journal of Coastal Research 94(sp1), 696-700, (9 September 2019). https://doi.org/10.2112/SI94-138.1
Received: 28 February 2019; Accepted: 2 April 2019; Published: 9 September 2019
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KEYWORDS
chebyshev polynomial approximation
hopf bifurcation
random parameter
Stochastic lorenz-family system
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