Mean first-passage time in a bistable system driven by multiplicative and additive colored noises with colored cross-correlation

First-passage time statistics in a bistable system subject to Poisson white noise by the generalized cell mapping method

“…In this problem, we are interested in when the system response crosses the boundary of safe domain for the first time, in other words, the computation of the probability density function (PDF) of first-passage time or the mean first-passage time (MFPT). Many research works on the first-passage time for random walks [1,2] and the MFPT in bistable systems [3,4] have been carried out, but most of them are first-order cases. In second-order and above systems, the exact solutions of the firstpassage time are usually not available.…”

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

“…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. In the study of tumor cell growth, mathematical model equations that closely captures the general features of tumor growth are considered in literature, and logistic equation is the most widely used deterministic model for theoretical study [13].…”

Effect of Internal Micro Environmental Fluctuations on Tumor Growth Dynamics

“…Noise effect on tumor growth especially the cross-correlated noises have been widely studied [6,7,8,9], and many complex properties of tumor growth process such as tumor extinction, response to therapy among others were reported at the influence of noise. The effect of noise especially correlated effects are the subject of many communications such as in bistable systems [10,11,12], in laser systems [1,14], in genetic networks [15,13], and in all these, many properties and system behaviors were studied and discovered. In a related communication, the direct effect of multiplicative colored noise on bacteria growth system was investigated using logistic growth model as a deterministic growth mechanism [16].…”