A Study of Nonlinear Dynamics in Mathematical Biology
作者： Joseph Ferrara
DOI:
关键词: Applied mathematics 、 Ode 、 Linearization 、 Stability (probability) 、 Nonlinear system 、 Ordinary differential equation 、 Mathematical and theoretical biology 、 Limit (mathematics) 、 Computer science 、 Dynamical systems theory
摘要: We rst discuss some fundamental results such as equilibria, linearization, and stability of nonlinear dynamical systems arising in mathematical modeling. Next we study the dynamics planar limit cycles, Poincare-Bendixson theorem, its useful consequences. then interaction between two three di erent cell populations, perform bifurcation analysis on systems. also analyze impact immunotherapy tumor population numerically.
unf.edu参考文章(11)
Leah Edelstein-Keshet, Mathematical Models in Biology Society for Industrial and Applied Mathematics. ,(2005) , 10.1137/1.9780898719147
Shiv Pillai, Abul K. Abbas, Andrew H. Lichtman, Cellular and Molecular Immunology ,(1994)
Stephen Smale, Morris W. Hirsch, Differential Equations, Dynamical Systems, and Linear Algebra ,(1974)
V KUZNETSOV, I MAKALKIN, M TAYLOR, A PERELSON, Nonlinear dynamics of immunogenic tumors: Parameter estimation and global bifurcation analysis Bulletin of Mathematical Biology. ,vol. 56, pp. 295- 321 ,(1994) , 10.1016/S0092-8240(05)80260-5
Fred Brauer, Carlos Castillo-Chavez, Carlos Castillo-Chavez, Mathematical Models in Population Biology and Epidemiology ,(2001)
D.E. Kirschner, T.L. Jackson, J.C. Arciero, A mathematical model of tumor-immune evasion and siRNA treatment Discrete and Continuous Dynamical Systems-series B. ,vol. 4, pp. 39- 58 ,(2003) , 10.3934/DCDSB.2004.4.39
G Oster, J Guckenheimer, The Hopf Bifurcation and Its Applications ,(1976)
Denise Kirschner, John Carl Panetta, Modeling immunotherapy of the tumor-immune interaction. Journal of Mathematical Biology. ,vol. 37, pp. 235- 252 ,(1998) , 10.1007/S002850050127
May Rm, Stability and complexity in model ecosystems. Monographs in population biology. ,vol. 6, pp. 1- 235 ,(1973)
Asad Usman, Chris Cunningham, None, Application of the Mathematical Model of Tumor-Immune Interactions for IL-2 Adoptive Immunotherapy to Studies on Patients with Metastatic Melanoma or Renal Cell Cancer Rose–Hulman Undergraduate Mathematics Journal. ,vol. 6, pp. 9- ,(2005)