Periodic solutions for discrete predator-prey systems with the Beddington-DeAngelis functional response.

*(English)*Zbl 1140.92325From the paper: Predator-prey interaction is one of the major forces shaping food webs. Since the great work of Lotka (in 1925) and Volterra (in 1926), modelling these interactions has been one of the central themes in mathematical ecology. One significant component of the predator-prey relationship is the predator’s rate of feeding upon prey, i.e., the socalled predator’s functional response. In general, the functional responses can be either prey dependent or predator dependent. Functional response equations that are strictly prey dependent, such as the Holling family ones, are predominant in the literature. It is well known that the discrete time models governed by difference equations are more appropriate than the continuous ones when the populations have nonoverlapping generations. In addition, discrete time models can also provide efficient computational models for numerical simulations. However, no such work has been done for predator-prey systems with the Beddington-DeAngelis functional response.

Here, sufficient criteria are established for the existence of positive periodic solutions of discrete nonautonomous predator-prey systems with the Beddington-DeAngelis functional response using a continuation theorem.

Here, sufficient criteria are established for the existence of positive periodic solutions of discrete nonautonomous predator-prey systems with the Beddington-DeAngelis functional response using a continuation theorem.

##### MSC:

92D40 | Ecology |

39A11 | Stability of difference equations (MSC2000) |

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\textit{J. Zhang} and \textit{J. Wang}, Appl. Math. Lett. 19, No. 12, 1361--1366 (2006; Zbl 1140.92325)

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##### References:

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