bifurcation theory in dynamical systems
Bifurcation theory in dynamical systems is a branch of mathematics that studies the sudden qualitative changes that occur in a system's behavior as one or more parameters are varied. It focuses on understanding how small changes in input can lead to large and often unexpected changes in the system's dynamics, including the emergence of new stable or unstable states, periodic or chaotic behavior, and the formation of patterns.
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Related Concepts (21)
- bifurcation phenomena
- bifurcations
- catastrophe theory
- chaos theory
- complex dynamics
- continuation methods
- fold bifurcation
- heteroclinic bifurcation
- hopf bifurcation
- limit cycles
- lyapunov exponents
- nonlinear systems
- periodic orbits
- pitchfork bifurcation
- poincaré-bendixson theorem
- saddle-node bifurcation
- stability analysis
- stability switching
- strange attractors
- symmetry breaking
- turing patterns
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