Nonlinear Oscillations in a Three-Dimensional Competition with Inhibition Responses in a Bio-Reactor

A three-dimensional bio-reactor model of exploitative competition of two predator organisms with inhibition responses for the same renewable organism with reproductive properties is considered. By using a Lyapunov function and the center manifold theorem the global stability, the existence of Hopf bifurcation and limit cycles are proved. This result is useful in understanding the nonlinear oscillation phenomena in bio-engineering.