Welcome to this Dynamical Systems Tutorial that provides a detailed introduction to Coupled Oscillatory Dynamics by taking you through the well known Kuramoto model of Coupled Oscillators in a step-by-step manner.
Section 1. The Introduction of the tutorial gives you a few basic facts about the Kuramoto model, and tries to provide some justification for the uses and importance of studying the dynamics of coupled oscillators.
Section 2. Derivation of the Kuramoto model will take you through the derivation of the Kuramoto model and will help to justify it's use in representing complex dynamical systems with relatively simple coupled equations.
Section 3. Kuramoto introduces the model itself, going into depth with regards to methods of analysing the model and predicting the model's dynamics. We also give some specific examples of it's uses in the real world, and finish by giving you a Java Applet to see the model in action.
Section 4. Simulator presents to the user a Java Applet which allows them to run Kuramoto simulations from right within their web-browser with up to 50-100 oscillators simultaneously and to tweak values while the simulation is running.
Section 5. Modifications briefly touches upon some of the modifications that have been made to the Kuramoto model to make it useful for more specific applications or in an attempt to add further control mechanisms or richer dynamics to the system.
Section 6. References provides references that have been used within this tutorial.
Section 1. The Introduction of the tutorial gives you a few basic facts about the Kuramoto model, and tries to provide some justification for the uses and importance of studying the dynamics of coupled oscillators.
Section 2. Derivation of the Kuramoto model will take you through the derivation of the Kuramoto model and will help to justify it's use in representing complex dynamical systems with relatively simple coupled equations.
Section 3. Kuramoto introduces the model itself, going into depth with regards to methods of analysing the model and predicting the model's dynamics. We also give some specific examples of it's uses in the real world, and finish by giving you a Java Applet to see the model in action.
Section 4. Simulator presents to the user a Java Applet which allows them to run Kuramoto simulations from right within their web-browser with up to 50-100 oscillators simultaneously and to tweak values while the simulation is running.
Section 5. Modifications briefly touches upon some of the modifications that have been made to the Kuramoto model to make it useful for more specific applications or in an attempt to add further control mechanisms or richer dynamics to the system.
Section 6. References provides references that have been used within this tutorial.
