Browse Hierarchy MTH744P: Dynamical Systems

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A dynamical system is any system which evolves over time according to some deterministic rule: all future states are determined by the present state in conjunction with the rule which determines the system's evolution. In discrete time, a dynamical system might evolve by the repeated application of a map; in continuous time, it might evolve according to a flow or a differential equation. Dynamical systems are therefore a fundamental tool in modelling real-world phenomena in the sciences. In this module we investigate the qualitative behaviours of dynamical systems in continuous time, considering questions such as: what features does the future evolution from a given point have? How does this future trajectory of the system depend on the initial state? If the dynamical system's underlying rule is itself changed, how do the qualitative features of its trajectories change?

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