Phase Portraits and bifurcation of Planar Autonomous Systems
Budget: £20 – £250 GBP
Project description:
Two dimensional systems of differential equations are very basic in the sense that
many real world problems can be modelled by such systems. What is the theory
behind the production of a phase portrait? How is a phase portrait produced? What is
the use of a phase portrait? What conclusions can be drawn from a phase portrait?
You will answer these questions in this project by choosing some particular systems,
including second order nonlinear equations, that you are interested in. You may also
explore phase portraits of systems with a parameter and analyse the bifurcation
behaviour. MAPLE may be used but you will expect to learn analytical methods.
Two dimensional systems of differential equations are very basic in the sense that
many real world problems can be modelled by such systems. What is the theory
behind the production of a phase portrait? How is a phase portrait produced? What is
the use of a phase portrait? What conclusions can be drawn from a phase portrait?
You will answer these questions in this project by choosing some particular systems,
including second order nonlinear equations, that you are interested in. You may also
explore phase portraits of systems with a parameter and analyse the bifurcation
behaviour. MAPLE may be used but you will expect to learn analytical methods.