The Study Of Stochastic And Delay Effects In Typical Biological And Chemical Systems

In this thesis, the stochastic and delay effects of typical biological and chemical sys-tems is investigated. We firstly introduce the research status of the systems involved in this paper, including comK gene expression system, Schlogl chemical reaction system and tu-mor growth system under immune surveillance. Then, in Chapter 2, the related stochastic and delay theory and the methods of analytical approximation and stochastic simulation are also introduced. By virtue of small delay approximation theory and stochastic simu-lation, in terms of stationary probability density (SPD), mean first passage time (MFPT) and signal-to-noise ratio (SNR), the dynamic behaviors of different systems are analyzed. The following results show:In Chapter 3, the research for ComK gene expression system shows:The impacts of time delay and noise on the autoregulatory gene expression involving a single gene are very complex and various. This thesis focuses on the impacts of multiplicative(σm) and additive(σA) noise intensities, cross-correlation intensity A between two noises, time delays r in the degradation process and θ in the synthesis process, and time delay β in both processes on the SPD and MFPT are discussed, respectively. These results indicate that (1) the regime shifts from high (or low) protein concentration state to low (or high) one can be induced by σm, λ and θ (or σ A and β); (2) the MFPT as a function of the noise intensity σM (or σA) exhibits one maximum value in the case of λ> 0 or θ> 0, this maximum is a signature of the noises enhanced stability phenomenon for high protein concentration state; and (3) T andβ can weaken the stability of high protein concentration state, on the contrary, A and θ can enhance it in the gene expression dynamic.In Chapter 4, the research for Schlogl chemical reaction systems indicates:(1) mul-tiplicative noise intensity D (or additive noise intensity Q) can induce the switch from high (or low) concentration state to low (or high) concentration one; (2) Furthermore, the quantitative analyses of the noise parameters and delayed feedback on the MFPT are discussed. The MFPT of switch as functions of the noise intensities exhibits a max-imum. The cross-correlation intensity between two noises λ, time delay T or strength K of the feedback loop can enhance the stability of the high concentration state; (3)Final-ly, the SNR as functions of system parameter μ exhibits a maximum, the existence of the maximum is a characteristic of the parametric resonance phenomenon. The increases of D can enhance the parametric resonance phenomenon at firstly and then weakens it. The increases of Q can weaken the parametric resonance phenomenon. The SNR as a function of D exhibits only a maximum, however for the case of SNR as a function of Q exhibits not only a maximum, but also a minimum. The existence of the maximum and minimum in the SNR are the identifying characteristics of the stochastic resonance and reverse-resonance phenomenon。(?), K and λ can enhance the stochastic resonance phenomenon, and weaken stochastic reverse-resonance phenomenon.In Chapter 5, the research for tumor growth system under immune surveillance shows: (1) In the case of tumor growth system under immune surveillance driven by colored noise, self-correlation times T1 and T2, cross-correlation intensity λ and time T3 between two noises can promote the growth of tumor cells; (2) Stochastic resonance, stochastic reverse-resonance and double stochastic resonance phenomenon can be found in tumor growth system under immune surveillance; (3) In the case of tumor growth system under immune surveillance driven by colored noise, increase of λ, T1 and T3 weaken the stochastic resonance and stochastic reverse-resonance, conversely, increase of T2 enhances stochastic resonance and stochastic reverse-resonance; (4) In the case of tumor growth system under immune surveillance driven by noise and time delay, under the consideration of the multi-plicative periodic signal, the time delay can induce a transition between the phenomenon of single and double stochastic resonance; when considering the additive periodic signal, the time delay can induce a transition between the phenomenon of stochastic resonance and stochastic resonance to disappear.