Analysis of bistable and oscillating reaction systems in presence of an external noise

Abstract

The paper analyses a bistable and an oscillatory reaction system in the presence of an external noise. The analysis of a bistable system shows that in the normal way the inclusion of noise destroys all the deterministic solutions. In other words, the stochastic system does not admit any solution. With imposition of certain restraints it is possible, however, to get stochastic solutions in a certain region of parameter space, which in general shrinks with the extent of noise. The modality of diminishing the region of solutions is different for white and nonwhite noise and has been discussed The paper also evaluates the influence of white and nonwhite noise on the behavior of an oscillating system and illustrates it by considering two case examples. One example indicates the conflicting role of white and nonwhite noise in bringing about the transitions from the oscillatory behavior while the second example shows no influence of white and nonwhite noise on the oscillating solution The implications of the role of noise in analysing bistable and oscillatory systems is discussed.