English abstract
In any environment, current reproduction of prey population will affect future population size, but these future changes may also affect the current reproductive decisions. We propose the dynamics of predator-prey cycles by two theoretical models based on field and laboratories experiments. These represent the suppression of breeding by prey in response to increase in predation pressure. On the other hand, non-breeding prey individuals have a better chance of avoiding predation than those in a reproductive state. The predator consumes both the breeder and suppressor individuals and this prey population is more prone to predation at higher densities. We showed that all the solutions of the first model of the project that initiate in R, are confined in this region under a condition. The stability analysis has been carried out for the equilibrium set for both models. We found out that Hopf bifurcation will occur by varying a parameter qı which represents the per capita rate of movement from breeding population into the suppressor population in the first model. 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 finding in the light of the Fennoscandian vole cycle. The theoretical results are compared with the numerical results for different sets of parameters.
