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Chaotic dynamics of a delayed tumor immune interaction model

International Journal of Biomathematics 2020年第2期13卷 1-33页

作者： subhas khajanchi Departrrert of Matherratics Presidercg Uriversity Kolkata 700073India

Due to the unpredictable growth of tumor cells,the tumor-immune interactive dynamics continues to draw attention from both applied mathematicians and ***-ematical modeling is a powerful tool to improve our understanding of the complicated biological system for tumor *** this goal,we report a mathematical model which describes how turmor cells evolve and survive the brief encounter with the immune system mediated by immune effector cells and host cells which includes discrete time *** analyze the basic mathematical properties of the considered model such as positivity of the system and the boundedness of the *** analyzing the distri-bution of eigenvalucs,local stability analysis of the biologically feasible equilibria and the existence of Hopf bifurcation are obtained in which discrete time delay is used as a bifurcation *** on the normal form theory and center manifold theorem,we obtain explicit expressions to determine the direction of Hopf bifurcation and the stability of Hopf bifurcating periodic *** simulations are carried out to illustrate the rich dynamical behavior of the delayed tumor *** model simula-tions demonstrate that the delayed tumor model exhibits regular and irregular periodic oscillations or chaotic behaviors,which indicate the scenario of long-term tumor relapse.

关键词： Tumor-immune interactions delay differential equations Hopf bifurcation chaos limit cycle

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Insight of Viral Infection of Jatropha Curcas Plant(Future Fuel):A control based mathematical study

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应用泛函分析学报 2011年第4期13卷 366-374,412页

作者： Sumit Nandi subhas khajanchi Amar Nath Chatterjee Priti Kumar Roy Department of Chemistry Narula Institute of TechnologyKolkata-700109 Center for Mathematical Biology and Ecology Department of MathematicsJadavpur UniversityKolkata-700032 India

Jatropha Curcas Linnaeous(Jatropha Curcas L)is a wonder plant with a variety of applications and enormous economic ***,an alternative fuel from non edible vegetable oil of Jatropha Curcas plant,has the requisite potential of providing a promising and commercially viable alternative to diesel oil since it has the desirable physicochemical and performance characteristics comparable to *** alternative fuel is eco-friendly,cost effective and has the huge potentiality for the future generations throughout the *** effective cultivation of this plant, protection from different viral diseases is *** this paper,we describe the eco-epidemiological model of the plant Jatropha Curcas L for understanding the disease dynamics which helps to control the viral infection of the Jatropha Curcas plant *** this approach,this plant can grow ideally for the renewable green fuel of the future world.

关键词： Jatropha Curcas cell biodiesel asymptotic stability optimal control remedial application

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