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Complexity analysis research of financial and economic system under the condition of three parameters’ change circumstances. (English) Zbl 1268.34084

Summary: This paper studies the characteristics of a series of complex systems, which are in combination of interest rate, investment, and price index parameters meeting the condition \(c-b-abc\geq0\), including stable node, saddle points, bifurcation, Hopf bifurcation, and chaos, and the corresponding mathematical expressions of Lyapunov index are given. Based on this, we perform complexity analysis of the system and study the change circumstances of Lyapunov index when one or two parameters synchronously change. Numerical simulation results verify the theoretical analysis and conclusion. The results of this economic and financial system provide reference to practical problems, and have a positive effect on the actual application of the system of this type.

MSC:

34C28 Complex behavior and chaotic systems of ordinary differential equations
93D30 Lyapunov and storage functions
34D08 Characteristic and Lyapunov exponents of ordinary differential equations
34C23 Bifurcation theory for ordinary differential equations
91G80 Financial applications of other theories
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