On the Bifurcation Analysis of a Food Web of Four Species Export

@article{citeulike:5946530, abstract = {This paper is concerned with bifurcations of equilibria and the chaotic dynamics of a food web containing a bottom prey X , two competing predators Y and Z on X , and a super predator W only on Y . Conditions for the existence of all equilibria and the stability properties of most equilibria are derived. A two-dimensional bifurcation diagram with the aid of a numerical method for identifying bifurcation curves is constructed to show the bifurcations of equilibria. We prove that the dynamical system possesses a line segment of degenerate steady states for the parameter values on a bifurcation line in the bifurcation diagram. Numerical simulations show that these degenerate steady states can help to switch the stabilities between two far away equilibria when the system crosses this bifurcation line. Some observations concerned with chaotic dynamics are also made via numerical simulations. Different routes to chaos are found in the system. Relevant calculations of Lyapunov exponents and power spectra are included to support the chaotic properties.}, author = {Wei, Hsiu-Chuan}, citeulike-article-id = {5946530}, citeulike-linkout-0 = {http://dx.doi.org/10.1016/j.amc.2009.10.016}, citeulike-linkout-1 = {http://linkinghub.elsevier.com/retrieve/pii/S0096300309009163}, day = {13}, doi = {10.1016/j.amc.2009.10.016}, issn = {00963003}, journal = {Applied Mathematics and Computation}, keywords = {bifurcations, chaotic\_systems, food\_web, lyapunov\_exponents, predator, prey, stability\_analysis}, month = {October}, posted-at = {2009-11-04 11:34:34}, priority = {2}, title = {On the Bifurcation Analysis of a Food Web of Four Species}, url = {http://dx.doi.org/10.1016/j.amc.2009.10.016}, year = {2009} }

TY - JOUR ID - citeulike:5946530 L3 - citeulike-article-id:5946530 N2 - This paper is concerned with bifurcations of equilibria and the chaotic dynamics of a food web containing a bottom prey X , two competing predators Y and Z on X , and a super predator W only on Y . Conditions for the existence of all equilibria and the stability properties of most equilibria are derived. A two-dimensional bifurcation diagram with the aid of a numerical method for identifying bifurcation curves is constructed to show the bifurcations of equilibria. We prove that the dynamical system possesses a line segment of degenerate steady states for the parameter values on a bifurcation line in the bifurcation diagram. Numerical simulations show that these degenerate steady states can help to switch the stabilities between two far away equilibria when the system crosses this bifurcation line. Some observations concerned with chaotic dynamics are also made via numerical simulations. Different routes to chaos are found in the system. Relevant calculations of Lyapunov exponents and power spectra are included to support the chaotic properties. JF - Applied Mathematics and Computation SN - 00963003 TI - On the Bifurcation Analysis of a Food Web of Four Species KW - bifurcations KW - chaotic_systems KW - food_web KW - lyapunov_exponents KW - predator KW - prey KW - stability_analysis AU - Wei, Hsiu-Chuan PY - 2009/10/13/ UR - http://dx.doi.org/10.1016/j.amc.2009.10.016 ER -