Narrow Results

We develop a 2-D discrete model to simulate malignant cells growing in healthy tissues using a thermodynamic method on the basis of Potts model. After introducing a malignant seed in a healthy tissue, we use a set of adjustment factors, including the interaction between cells and nutrient, to simulate the growth of malignant cells under different environments. This allows us to investigate the effects of environment on malignant cell growth and the formation of cancer.

An analysis is made on a three dimensional mathematical model for the interaction of nutrient, phytoplankton and their predator zooplankton population in an open marine system. For a realistic representation of the open marine plankton ecosystem, we have incorporated various natural phenomena such as dissolved limiting nutrient with general nutrient uptake function, nutrient recycling, interspecies competition and grazing at a higher level. For the model with constant nutrient input and different constant washout rates, conditions for boundedness of the solutions, existence and stability of non negative equilibria, as well as persistence are given. The model system is studied analytically and the threshold values for the existence and stability of various steady states are worked out. It is observed that if the dilution rate of nutrient crosses certain critical value, the system enters into Hopf-bifurcation. Finally, it is observed that planktonic bloom can be controlled and stability around the equilibrium of coexistence can be obtained if the dilution rate of phytoplankton population is increased. Computer simulations have been carried out to illustrate different analytical results.

We consider a phytoplankton–zooplankton interaction model which depends on two complementary nutrients. For a realistic representation in chemostat plankton ecosystem, we have incorporated various natural phenomena such as dissolved limiting nutrients with nutrient uptake functions and yield constants. For the model with two different constant nutrient inputs with same constant washout rate, existence and stability of non-negative equilibria as well as persistence are given. We analyze the behavior of solution of model in order to answer the biological question and seek to determine the limiting behavior of the surviving organisms and the nutrients. It is observed that the constant nutrient inputs of two complementary nutrients play an important role to change steady state behavior of the system. Further it is observed that if the dilution rate of chemostat crosses certain critical value, the system enters into Hopf-bifurcation. Finally, we have derived the explicit algorithm which determines the direction of Hopf-bifurcation. Computer simulations have been carried out to illustrate different analytical results.

This paper deals with a nutrient-phytoplankton-zooplankton ecosystem model consisting of dissolved limiting nutrient with nutrient uptake functions. We use a Holling type-II harvest function to model density dependent plankton population. It is assumed that phytoplankton release toxic chemical for self defense against their predators. The model system is studied analytically and the threshold conditions for the existence and stability of various steady states are worked out. It is observed that if the rate of toxin produced by phytoplankton population crosses a certain critical value, the system enters into Hopf bifurcation. We have derived the direction of Hopf-bifurcation. Our observations indicate that constant nutrient input and the maximal zooplankton conversion rate influence the nutrient-plankton ecosystem model and maintain stability around the coexistence equilibrium in the presence of toxic chemical release by phytoplankton for self defense. It is observed that harvesting rates of the plankton population play a vital role in changing the stability criteria. Computer simulations have been carried out to illustrate different analytical results.

The nutrient of 2-year-old Dendrobium officinale Kimura et Migo from four different latitudes Weifang City, Shandong Province (36°78'N, 119°02'E), Wujiang City, Jiangsu Province (31°08'N, 120°66'E), Wenzhou City, Zhejiang Province (28°27'N, 121°05'E) and Menghai City, Yunnan Province (21°59'N, 100°24'E) was analyzed in order to understand the effect of latitude, temperature, humidity, light intensity on its nutrient. The results showed that the ecological factors had effects on the nutrient of 2-year-old D. officinale. The nutrient copper and zinc content increased with the increase of latitude, effective accumulated temperature. The magnesium and zinc increased with the increase of humidity. The nutrient of 2-year-old D. officinale in WF equals to or is higher than that in the other places.