Functions and Analysis

    

Methods of Nonlinear Bifurcation Geometry in the Study of Nonautonomous Scalar Equations

Authors: Alexander C. Sarich

The study of nonautonomous scalar equations comprises a subset of solutions defining the regions of stability and instability inherent to a system. Under specific shifts in the variables of such equations, those referring to a scalar parameter, the quantity of stability points may vary. The exact value at which the quantity of stability points changes, refers to a bifurcation in the system. When a specific function, or set of functions, cannot be solved exactly through algebraic methods, an equivalence to geometric structures may provide intuitive connections to a more abstract topology that solves for those values exactly. Examples considered include˙ x = x−x2e−1(1 + t2)−1, and the Spruce-Budworm and Forest Model.

Comments: 19 Pages.

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[v1] 2025-01-06 20:56:33

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