Nonlinear Analysis: Real World Applications 7 (2006) 1193 – 1204 www.elsevier.com/locate/na Existence of periodic solutions in predator–prey and competition dynamic systems  Martin Bohner a , ∗ , Meng Fan b , Jimin Zhang b a Department of Mathematics and Statistics, University of Missouri–Rolla, Rolla, MO 65401, USA b School of Mathematics and Statistics, and Key Laboratory forVegetation Ecology, Northeast Normal University, Changchun, Jilin 130024, PR China Received 30 October 2005; accepted 1 November 2005 Abstract In this paper, we systematically explore the periodicity of some dynamic equations on time scales, which incorporate as special cases many population models (e.g., predator–prey systems and competition systems) in mathematical biology governed by differ- ential equations and difference equations. Easily verifiable sufficient criteria are established for the existence of periodic solutions of such dynamic equations, which generalize many known results for continuous and discrete population models when the time scale T is chosen as R or Z, respectively. The main approach is based on a continuation theorem in coincidence degree theory, which has been extensively applied in studying existence problems in differential equations and difference equations but rarely applied in dynamic equations on time scales. This study shows that it is unnecessary to explore the existence of periodic solutions of continuous and discrete population models in separate ways. One can unify such studies in the sense of dynamic equations on general time scales.  2005 Elsevier Ltd. All rights reserved. MSC: 92D25; 39A12 Keywords: Time scales; Periodic solution; Coincidence degree; Predator–prey system; Beddington–DeAngelis response; Holling-type response; Competition system; Gilpin–Ayala system 1. Introduction In the past decades, mathematical ecology has seen much progress, especially in population dynamics. Most natural environments are physically highly variable, and in response, birth rates, death rates, and other vital rates of populations, vary greatly in time. Theoretical evidence to date suggests that many population and community patterns represent intricate interactions between biology and variation in the physical environment (see [4] and other papers in the same issue). Therefore, the focus in theoretical models of population and community dynamics must be not only on how populations depend on their own population densities or the population densities of other organisms, but also on how  Supported by the National Natural Science Foundation of PR China (No. 10201005), the Key Project on Science and Technology of the Education Ministry of PR China, and the University of Missouri Research Board. ∗ Corresponding author. Tel.: +1 573 341 6208; fax: +1 573 341 4741. E-mail addresses: bohner@umr.edu (M. Bohner), mfan@nenu.edu.cn (M. Fan). 1468-1218/$ - see front matter  2005 Elsevier Ltd. All rights reserved. doi:10.1016/j.nonrwa.2005.11.002