5 papers
A Saturation-Based Optimal Velocity Model for Traffic Flow Dynamics
Nizhum Rahman, Trachette L. Jackson
Many headway-based car-following models describe longitudinal adaptation through linear relaxation laws, which can produce unrealistically large accelerations and limit the physica…
Front stability of infinitely steep travelling waves in population biology
Matthew J Simpson, Nizhum Rahman, Alexander KY Tam
Reaction-diffusion models are often used to describe biological invasion, where populations of individuals that undergo random motility and proliferation lead to moving fronts. Man…
Survival, extinction, and interface stability in a two--phase moving boundary model of biological invasion
Matthew J Simpson, Nizhum Rahman, Scott W McCue +1
We consider a moving boundary mathematical model of biological invasion. The model describes the spatiotemporal evolution of two adjacent populations: each population undergoes lin…
Classification and stability analysis of polarising and depolarising travelling wave solutions for a model of collective cell migration
Nizhum Rahman, Robert Marangell, Dietmar Oelz
We study travelling wave solutions of a 1D continuum model for collective cell migration in which cells are characterised by position and polarity. Four different types of travelli…
A note on the Sine-Gordon expansion method and its applications
Nizhum Rahman
The sine-Gordon expansion method; which is a transformation of the sine-Gordon equation has been applied to the potential-YTSF equation of dimension (3+1) and the reaction-diffusio…