An investigation on Michaelis-Menten kinetics based complex dynamics of tumor-immune interaction. (English) Zbl 1483.92074
Summary: We investigate the dynamics of a three-dimensional tumor-immune interactions system. Local dynamics of the system has studied by the finding stability and Hopf bifurcation at biologically feasible equilibria. Further, chaotic phenomena have been investigated by measuring the asymptotic growth of the corresponding phase space trajectory with the various bifurcating parameters of the system. A dynamics of mean fluctuations of the tumor growth based on its local maxima have investigated under the same parameters. A significant correlation between the fluctuations and the tumor dynamics have verified by statistical analysis.
MSC:
| 92C45 | Kinetics in biochemical problems (pharmacokinetics, enzyme kinetics, etc.) |
| 34C60 | Qualitative investigation and simulation of ordinary differential equation models |
| 34D05 | Asymptotic properties of solutions to ordinary differential equations |
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