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
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
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
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
Saddle-node bifurcation
In the mathematical area of bifurcation theory a saddle-node bifurcation, tangential bifurcation or fold bifurcation is a local bifurcation in which two fixed points (or equilibria) of a dynamical sys
Bifurcation diagram
In mathematics, particularly in dynamical systems, a bifurcation diagram shows the values visited or approached asymptotically (fixed points, periodic orbits, or chaotic attractors) of a system as a f
Chaotic hysteresis
A nonlinear dynamical system exhibits chaotic hysteresis if it simultaneously exhibits chaotic dynamics (chaos theory) and hysteresis. As the latter involves the persistence of a state, such as magnet
Crisis (dynamical systems)
In applied mathematics and astrodynamics, in the theory of dynamical systems, a crisis is the sudden appearance or disappearance of a strange attractor as the parameters of a dynamical system are vari