Coarse Dynamics for Coarse Modeling: An Example From Population Biology

Entropy

Justin Bush¹ 

[1] Department of Mathematics, Hill Center-Busch Campus, Rutgers, The State University of New Jersey, 110 Frelinghuysen Rd, Piscataway, NJ 08854, USA; E-Mail:

关键词: database for dynamics;    conley theory;    population model;   

DOI  :  10.3390/e16063379

来源: mdpi

【 摘 要 】

Networks have become a popular way to concisely represent complex nonlinear systems where the interactions and parameters are imprecisely known. One challenge is how best to describe the associated dynamics, which can exhibit complicated behavior sensitive to small changes in parameters. A recently developed computational approach that we refer to as a database for dynamics provides a robust and mathematically rigorous description of global dynamics over large ranges of parameter space. To demonstrate the potential of this approach we consider two classical age-structured population models that share the same network diagram and have a similar nonlinear overcompensatory term, but nevertheless yield different patterns of qualitative behavior as a function of parameters. Using a generalization of these models we relate the different structure of the dynamics that are observed in the context of biologically relevant questions such as stable oscillations in populations, bistability, and permanence.

【 授权许可】

CC BY   
© 2014 by the authors; licensee MDPI, Basel, Switzerland