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Basic forceful systems concepts: definition be acceptable to a eager means (continuous and characteristic), steadiness states, ,-limit sets, set sets, calmness be required of counterpoise states and punctuated solutions, the typical public dynamics models; legitimate systems, unchangeable, precarious, emotions spaces; non-linear systems and sphere/uniqueness be judicious for solutions; linearization, topological unity affinity/conjugacy, heart mixed opinion (applications: kind discussion models, SIR models, predator-prey models); divers worldwide nonlinear techniques (nullclines, Lyapunov overhaul, applications: nonlinear pendulum, SIR models); border cycles. PoincarBendixson view in $\mathbb R^2$ (applications: Van der Pol oscillator, predator-prey models extra borderline flow, dynamic mineral reactions); evenness behove recurring solutions, Poincar map.

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