Category: Bifurcation theory

Period-doubling bifurcation
In dynamical systems theory, a period-doubling bifurcation occurs when a slight change in a system's parameters causes a new periodic trajectory to emerge from an existing periodic trajectory—the new
Bifurcation theory
Bifurcation theory is the mathematical study of changes in the qualitative or topological structure of a given family of curves, such as the integral curves of a family of vector fields, and the solut
Heteroclinic bifurcation
No description available.
Feigenbaum constants
In mathematics, specifically bifurcation theory, the Feigenbaum constants are two mathematical constants which both express ratios in a bifurcation diagram for a non-linear map. They are named after t
Biological applications of bifurcation theory
Biological applications of bifurcation theory provide a framework for understanding the behavior of biological networks modeled as dynamical systems. In the context of a biological system, bifurcation
Transcritical bifurcation
In bifurcation theory, a field within mathematics, a transcritical bifurcation is a particular kind of local bifurcation, meaning that it is characterized by an equilibrium having an eigenvalue whose
Homoclinic bifurcation
No description available.
Bogdanov–Takens bifurcation
In bifurcation theory, a field within mathematics, a Bogdanov–Takens bifurcation is a well-studied example of a bifurcation with co-dimension two, meaning that two parameters must be varied for the bi
Blue sky catastrophe
The blue sky catastrophe is a form of orbital indeterminacy, and an element of bifurcation theory.
Catastrophe theory
In mathematics, catastrophe theory is a branch of bifurcation theory in the study of dynamical systems; it is also a particular special case of more general singularity theory in geometry. Bifurcation
Spatial bifurcation
Spatial bifurcation is a form of bifurcation theory. The classic bifurcation analysis is referred to as an ordinary differential equation system, which is independent on the spatial variables. However
Pitchfork bifurcation
In bifurcation theory, a field within mathematics, a pitchfork bifurcation is a particular type of local bifurcation where the system transitions from one fixed point to three fixed points. Pitchfork
Hopf bifurcation
In the mathematical theory of bifurcations, a Hopf bifurcation is a critical point where a system's stability switches and a periodic solution arises. More accurately, it is a local bifurcation in whi
Infinite-period bifurcation
No description available.
Normal form (dynamical systems)
In mathematics, the normal form of a dynamical system is a simplified form that can be useful in determining the system's behavior. Normal forms are often used for determining local bifurcations in a