EFFECTS OF DELAY AND SEASONALITY ON TOXIN PRODUCING PHYTOPLANKTON-ZOOPLANKTON SYSTEM  

作　　者：SUNITA GAKKHAR ANURAJ SINGH BRAHAM PAL SINGH 

机构地区：[1]Department of MathematicsIndian Institute of Technology Roorkee Roorkee 247667, Uttarakhand, India [2]Department of Mathematics J. V. Jain Degree CollegeSaharanpur 2~001, U.P., India

出　　处：《International Journal of Biomathematics》2012年第5期239-259,共21页生物数学学报（英文版）

摘　　要：A dynamical model for toxin producing phytoplankton and zooplankton has been formu- lated and analyzed. Due to gestation of prey, a discrete time delay is incorporated in the predator dynamics. The stability of the delay model is discussed and Hopf bifurcation to a periodic orbit is established. Stability and direction of bifurcating periodic orbits are investigated using normal form theory and center manifold arguments. Global existence of periodic orbits is also established. To substantiate analytical findings, numerical simu- lations are performed. The system shows rich dynamic behavior including chaos and limit cycles. The influence of seasonality in intrinsic growth parameter of the phytoplankton population is also investigated. Seasonality leads to complexity in the system.

关 键 词：Time delay stability Hopf bifurcation period chaos. 

分 类 号：O415.5[理学—理论物理] Q178.53[理学—物理]