Dynamic complexities in an epidemic model with birth pulses and pulse culling

作者：Gao Shujing^*; Chen Lansun; Teng Zhidong; Xie Dehui

来源：International Journal of Bifurcation and Chaos, 2007, 17(2): 521-533.

DOI：10.1142/S0218127407017392

• epidemic model
• birth pulse
• pulse culling
• chaos
• period-doubling bifurcation
• period-halving bifurcation

In this paper, we propose a model for the dynamics of a fatal infectious disease in a wild animal population with birth pulses and pulse culling, where periodic birth pulses and pulse culling occur at different fixed times. Using the discrete dynamical system determined by stroboscopic map, we obtain an exact cycle of the system, and obtain the threshold conditions for its stability. Bifurcation diagrams are constructed with the birth rate ( or culling effort) as the bifurcation parameter, and these are observed to display complex dynamic behaviors, including chaotic bands with period windows, period-doubling and period-halving bifurcations, pitch-fork and tangent bifurcations, nonunique dynamics ( meaning that several attractors or attractor and chaos coexist), basins of attraction and attractor crisis. This suggests that birth pulses and pulse culling provide a natural period or cyclicity that makes the dynamical behaviors more complex. Moreover, we investigate the sufficient conditions for global stability of semi-trivial periodic solutions.

• 出版日期2007-2
• 单位大连理工大学; 新疆大学; 赣南师范大学