Constant and Crossing-Variable Polynomial Systems

Albert C. J. Luo ()
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Albert C. J. Luo: Southern Illinois University Edwardsville, Department of Mechanical and Mechatronics Engineering

Chapter Chapter 2 in 1-dimensional Flow Arrays and Bifurcations in Planar Polynomial Systems, 2024, pp 55-113 from Springer

Abstract: Abstract In this Chapter, consider dynamical systems with constant and crossing-univariate polynomial vector fields. The corresponding stability and bifurcation of the 1-dimensional flow is discussed. The $$(2m_{1} + 1)^{{{\text{th}}}}$$ ( 2 m 1 + 1 ) th order up-parabola and down-parabola flows in such a polynomial system are presented, which are also for the $$(2m_{1} + 1)^{{{\text{th}}}}$$ ( 2 m 1 + 1 ) th order up-parabola and down-parabola flows appearing and switching bifurcations. The $$(2m_{1} )^{{{\text{th}}}}$$ ( 2 m 1 ) th order increasing-inflection and decreasing-inflection flows in such a polynomial system are also obtained, which are the $$(2m_{1} )^{{{\text{th}}}}$$ ( 2 m 1 ) th order increasing-inflection and decreasing-inflection flows appearing and switching bifurcations of the up and down-parabola flows.

Date: 2024
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-981-97-2204-4_2

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DOI: 10.1007/978-981-97-2204-4_2

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