Aimed at the problem that the abundance level fluctuations of galactose affect the yeast phenotypes directly or indirectly, it is necessary to decode the regulation mechanism of the multi-scale noise mediated Gal4 gene coupling positive and negative feedback loops. In the report, the multi-source colored noise was introduced, an equivalent Fokker-Planck equation was constructed, the steady state probability distribution function and the mean first passage time was calculated, the relevant dynamic indicators were analyzed to reveal the system’s dynamic behavior, a sensitivity function was defined to evaluate the influence of each regulatory source from the perspective of systems theory. The results indicated that the galactose abundance level can directly modulate the stochastic bifurcation of the Gal4 gene expression system, and under the induction of colored noise, the changes of noise intensity and its autocorrelation time alter the peak structure of the probability distribution function and state-switching time, and the effects of multiplicative noise on the system was greater than that of additive noise.

In the report, the tumor cell growth model with non-Markovian characteristics was studied, and the memory scales were defined to characterize the non-Markovian dependence of tumor cell evolution. Firstly, the existence of an effective metastasis rate in the evolutionary process of tumor cells was demonstrated; secondly, the equivalence between memory networks and Markov networks was demonstrated. The equivalence depended on the controllability of memory scale, which induced the fluctuations of the growth process of tumor cells and normalized the theoretical expression of the noise in the tumor cell growth during the different processes. The numerical simulation results indicated that the memory scale in the cell mutations amplifies the noise level expressed by tumor cells; on the contrary, the memory scale during the phagocytosis process suppresses the noise of tumor progression, which suggested that the evolution of tumor cells is influenced by the dual effects of the memory levels.

In the report, the stability regulation mechanism of the Holling IV-Leslie predator-prey system under dichotomous noise was investigated. By characterizing the critical bifurcation conditions that lead to the instability induced by dichotomous noise, the effects of the noise intensity and the temporal memory on the system’s stability were analyzed, and it was demonstrated that adjusting temporal memory can expand the region of Turing instability more sensitively. The numerical simulation experiment results indicated that dichotomous noise destabilizes the system by reshaping bifurcation curves and inducing limit cycle oscillations.