Bifurcation Analysis for Polynomial Equations
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BANICHUK, Nikolay, BARSUK, Alexander A., JERONEN, J., TUOVINEN, Tero, NEITTAANMAKI, Pekka. Bifurcation Analysis for Polynomial Equations. In: Solid Mechanics and its Applications, 2020, nr. 259, pp. 33-68. ISSN 0925-0042. DOI: https://doi.org/10.1007/978-3-030-23803-2_2
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Solid Mechanics and its Applications
Numărul 259 / 2020 / ISSN 0925-0042

Bifurcation Analysis for Polynomial Equations

DOI: https://doi.org/10.1007/978-3-030-23803-2_2

Pag. 33-68

Banichuk Nikolay1, Barsuk Alexander A.2, Jeronen J.3, Tuovinen Tero3, Neittaanmaki Pekka3
 
1 Institut pe Probleme Mecanice, Academia de Stiinte a Rusiei,
2 Moldova State University,
3 Department of Mathematical Information Technology, University of Jyvaskyla
 
Disponibil în IBN: 27 martie 2021


Rezumat

This chapter is devoted to bifurcation problems based on some models described by polynomial equations with real coefficients. Bifurcation analysis, parametric representations of solutions and their asymptotic analysis and expressions are described within a framework of analytical approaches. The results presented in this chapter can be used to help locate the bifurcation points of the solution curves. The results also allow the development of very efficient procedures for sensitivity analysis of the dependences of solutions on the problem parameters.

Cuvinte-cheie
Asymptotic analysis, Bifurcation (mathematics), polynomials