Newman T J, Antonovics J, Wilbur H M
Department of Physics, University of Virginia, Charlottesville, Virginia 22903, USA.
Theor Popul Biol. 2002 Sep;62(2):121-8. doi: 10.1006/tpbi.2002.1584.
We consider the effect of coupling an otherwise chaotic population to a refuge. A rich set of dynamical phenomena is uncovered. We consider two forms of density dependence in the active population: logistic and exponential. In the former case, the basin of attraction for stable population growth becomes fractal, and the bifurcation diagrams for the active and refuge populations are chaotic over a wide range of parameter space. In the case of exponential density dependence, the dynamics are unconditionally stable (in that the population size is always positive and finite), and chaotic behavior is completely eradicated for modest amounts of dispersal. We argue that the use of exponential density dependence is more appropriate, theoretically as well as empirically, in a model of refuge dynamics.
我们考虑将一个原本混沌的种群与一个避难所耦合的影响。发现了一系列丰富的动力学现象。我们考虑活跃种群中两种形式的密度依赖性：逻辑斯蒂型和指数型。在前一种情况下，稳定种群增长的吸引盆变成分形，并且活跃种群和避难所种群的分岔图在广泛的参数空间范围内是混沌的。在指数密度依赖性的情况下，动力学是无条件稳定的（即种群大小始终为正且有限），并且对于适度的扩散量，混沌行为完全消除。我们认为，在避难所动力学模型中，从理论和经验角度来看，使用指数密度依赖性更为合适。
