Spatiotemporal Noise Dynamics In Nonlinear Biosystems

In this dissertation, using the methods of nonlinear dynamics and stochastic process in statistical physics, I have studied spatiotemporal noise dynamics in selected biosystems, e.g., tumor systems, prey-predator ecosystems and mutualism systems. This research has looked insight into the growth law of tumor cells and provided many illuminations to the traditional cancer therapy. At the same time, it is also suggested that the environmental protection is quite necessary in order to keep the balance and the stability of ecosystems. It includes three sections:1. The spatiotemporal noise effects on tumor systemsFirstly, I have studied the effect of additive and multiplicative noises on the growth of a tumor based on a logistic growth model. The steady-state probability distribution and the average population of the tumor cells were given to explain the important roles of correlated noises in the tumor growth. It had been reported that multiplicative noise induces a phase transition of the tumor growth from an uni-stable state to a bi-stable state; the relationship between the intensity of multiplicative noise and the population of the tumor cells shows a stochastic resonance-like characteristic. It was also confirmed that additive noise weakened rather than extinguished the tumor growth. Homologous noises, however, promoted the growth of a tumor. I also discussed about the relationship between the tumor treatment and the model.Secondly, considering the growth of tumor cells modeled by an enzyme dynamic process under an immune surveillance, I have studied in anti-tumor immunotherapy the single-variable growth dynamics of tumor cells subjected to a multiplicative noise and an external therapy intervention simultaneously. There are four main findings: (1) Two simulative parameters of therapy, i.e., therapy intensity and therapy duty-cycle, were introduced to characterize a treatment process similar to a tumor clinic therapy. There exists a critical therapy boundary which, in an exponent-decaying form, divides the parameter region of therapy into an invalid and a valid treatment zone, respectively. (2) A greater critical therapy duty-cycle is necessary to achieve a valid treatment for a lower therapy intensity while the critical therapy intensity decreases accordingly with an enhancing immunity. (3) The primary clinic observation of the patients with the typical non-hodgekin's lymphoma basically agreed with the dynamic simulations. (4) In an anti-tumor system modulated by a seasonal external field, for optimally selected values of the multiplicative noise intensity, stochastic resonance can be observed, which is manifested by the quasi-symmetry of two potential minima.Finally, the studies of one and two dimensional models of spatially extended anti-tumor system with a fluctuation in growth rate was carried out. It is suggested that the spatiotemporal noise, assumed to reflect the environmental fluctuation in a spatially extended tumor system, can induce nonequilibrium phase transition. In this thesis I introduce the structure factor to reveal the invasive tumor growth quantitatively. The multiplicative noise is found to have opposite effects: the positive effect on a non-excited tumor and the negative effect on an excited tumor. The homogenous environment can lead the tumor cells to expansive growth, while the inhomogenous environment may result in the infiltrative growth of the tumor cells. The different responses were determined by the level of environmental fluctuation.2. Correlated noises in ecosystemsI have investigated a Volterra ecosystem driven by correlated noises. The fluctuation in the death rate of the predator induces an increase in population densities of the predators. The fluctuation in the growth rate of the prey, however, leads the predators to decay. It is reported that the predators undergo sensitivity to a random environment, whereas the preys exhibit a surprising endurance to the same stochastic factor. The predators are of better stability under strong correlation of noises.Understanding the cause of the synchronization of population evolution is an important issue for ecological improvement. Here I present a Lotka-Volterra-type model driven by two correlated environmental noises and show, via theoretical analysis and direct simulation, that noise correlation can induce a synchronization of the mutualists. The time series of mutual species exhibit a chaotic-like fluctuation, which is independent of the noise correlation, however, the chaotic fluctuation of mutual species ratio decreases with the noise correlation. A quantitative parameter defined for characterizing chaotic fluctuation provides a good approach to measure when the complete synchronization happens. 3. Correlated noises induced order phenomenaHere I report the phenomenon of the nonequilibrium dynamical phase transition (NDPT) appearing in a kinetic Ising spin system (ISS) subjected to a joint application of a determinant external field and the stochastic mutually correlated noises simultaneously. For example, within the multi-parameter space, the dynamic order parameter takes on a stochastic resonance with reentrant trend against noise intensity. This method is expected to be applied in the biosystems with correlated noises.