Breeding adjustment of small mammals to avoid predation

We studied theoretical models based on field and laboratories experiments where due to short-term predation pressure small mammals suppress breeding and when the predation pressure eases the suppressor class starts breeding again. The predator consumes both the breeder and suppressor individuals and this prey population is more prone to predation at higher densities. The stability analysis has been carried out for the equilibrium set for two models, in terms of the values of combinations of these parameters. We found that Hopf bifurcation will occur by varying a parameter q1q1 which represents the rate by which breeder population turns suppressor population. It is found that predator induced breeding suppression (PIBS) acts to destabilize the stable interaction. We further examined the effect of time delay upon the stability of equilibrium in models. Using time delay as a bifurcation parameter it is shown that Hopf bifurcation could occur. We discussed these findings in the light of the Fennoscandian vole cycle. The theoretical results are compared with the numerical results for different sets of parameters.