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The branch of mathematics and physics that studies systems governed by nonlinear equations—systems where feedback, thresholds, and emergent behavior produce patterns that linear models cannot capture. Nonlinear dynamics encompasses chaos theory, complexity theory, bifurcation theory, and the study of attractors, fractals, and pattern formation. It's the mathematics of tipping points, of systems that can suddenly flip from one state to another, of structures that emerge spontaneously from disorder, of behaviors that are deterministic yet unpredictable. Nonlinear dynamics provides the tools for understanding everything from heartbeats to ecosystems to economies—systems that are neither fully random nor fully predictable, where the same rules can produce wildly different outcomes depending on initial conditions.
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