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The goal of this paper is to establish the uniqueness of limit cycles of the predator-prey systems with Beddington-DeAngelis functional response. Through a change of variables, the predator-prey system can be transformed into a better studied Gause-type predator-prey system. As a result, the uniqueness of limit cycles can be solved.

In this paper we study the Hopf bifurcation for the Holling-Tanner model, a well-known predator-prey model in mathematical ecology. We show that for some parameter ranges, the Hopf bifurcation is subcritical and thus the system may have multiple limit cycles.

In this paper we derive some results to ensure that the number of the limit cycle of a generalized Gause-type predator᎐prey system does not exceed one. Two examples are presented in the final section.

SynopsisWe study Berman's problemsubjects to the conditions f(0) =f″(0) = f′(1) = f(1)− 1 = 0, which arises from the study of laminar flows in channels with porous walls. Positive (negative) Re denotes the case of suction (injection) flows. Preliminary numerical studies indicated the existence of three different types of solutions and a small portion of mathematical evidence was provided. In this paper, we are able to show that there exist connected sets in the Re-K plane on which different types of solutions occur. In particular, our result verifies that the problem possesses all three types of suction solutions for sufficiently large Re. Moreover, the limiting injection solution is also obtained.