J. Appl. Math. Comput. DOI 10.1007/s12190-014-0838-6 ORIGINAL RESEARCH Dynamical behaviors of fractional-order Lotka–Volterra predator–prey model and its discretization A. A. Elsadany · A. E. Matouk Received: 25 January 2014 © Korean Society for Computational and Applied Mathematics 2014 Abstract In this work, we study the dynamical behaviors of fractional-order Lotka– Volterra predator–prey system and its discretized counterpart. It is shown that the discretized system exhibits much richer dynamical behaviors than its corresponding fractional-order form; in the discretized system, many types of bifurcations (transcriti- cal, flip, Neimark–Sacker) and chaos are obtained however the dynamics of fractional- order counterpart is included only stable (unstable) equilibria. Numerical simulations are used to verify the correctness of the analytical results. Keywords Fractional-order · Lotka–Volterra predator–prey system · Discretization · Bifurcations · Chaos 1 Introduction Recently, population models have increasing attention by scientists due to their uni- versal existence and importance [1]. Indeed, there are different approaches to study population models, e.g. ordinary differential equations, difference equations, partial Dedicated to Prof. E. Ahmed on the Occasion of his 60th Birthday. A. A. Elsadany Department of Basic Science, Faculty of Computers and Informatics, Suez Canal University, Ismailia 41522, Egypt A. A. Elsadany (B ) Department of Mathematics, Shanghai University, Shanghai 200444, China e-mail: aelsadany1@yahoo.com A. E. Matouk Mathematics Department, Faculty of Science, Hail University, Hail 2440, Saudi Arabia e-mail: aematouk@hotmail.com 123