Topic
Bifurcation diagram
About: Bifurcation diagram is a research topic. Over the lifetime, 8379 publications have been published within this topic receiving 139664 citations.
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01 Jan 1978
94 citations
TL;DR: In this paper, a system of ODEs which describes the transmission dynamics of childhood diseases is considered, and a three-parameter unfolding of the normal form is studied to capture possible complex dynamics of the original system which is subjected to certain constraints on the state space due to biological considerations.
93 citations
TL;DR: In this article, a qualitative change in the structural behaviour of the system is called bifurcation. But this qualitative change is difficult to quantify. And it is not always possible to predict the number and stability of equilibria.
93 citations
TL;DR: In this paper, it is shown that the structure of the 2D and 3D parameter spaces can be simply described using the concept of multi-parametric bifurcations.
Abstract: In this work a one-dimensional piecewise-linear map is considered. The areas in the parameter space corresponding to specific periodic orbits are determined. Based on these results it is shown that the structure of the 2D and 3D parameter spaces can be simply described using the concept of multi-parametric bifurcations. It is demonstrated that an infinite number of two-parametric bifurcation lines starts at the origin of the 3D parameter space. Along each of these lines an infinite number of bifurcation planes starts, whereas the origin represents a three-parametric bifurcation.
93 citations
TL;DR: In this article, the authors focus on the computational analysis of partial differential equations with emphasis on the stability of the equilibrium states and on their bifurcations, and demonstrate the effectiveness of this technique by computing interesting new dynamics in a relatively simple hydrodynamic system.
93 citations