Effects of periodic force on the stability of the metastable state in logistic system

Steady state analysis for the effect of tumor microenvironmental factors on tumor growth dynamics driven by correlated noises

“…Theoretical description of these systems requires a link between deterministic equations and stochastic process. In application, the theoretical model equation is the Langevin stochastic equation and the corresponding Fokker Planck equation for the time evolution of probability density, and such theoretical descriptions have been used in different context to study the behavior of noise driven systems [1][2][3], where the driven noises are either Gaussian white or colored noises and in the form of additive or multiplicative. Research in [4] first discovered that physical systems driven by simultaneous noises with common origin leads to correlated effects, and the study of complex systems driven by correlated noises have been given much attention especially in bistable system [5][6][7], in mode laser system [8,9], in gene selection and genetic transcription regulatory models [10][11][12] and in all these systems, interesting properties and system behaviors were discovered at the influence of noise correlated effects.…”