Effects of self-correlation time on stability of metastable state in logistic model

In this paper, we study stationary probability distribution and stochastic resonance phenomenon in a tumor model under immune surveillance, which is driven by colored Gaussian noises. The signal-to-noise ratio is calculated when periodic signal is introduced. The impacts of self-correlation times s 1 and s 2 , cross-correlation strength k between two noises and time s 3 on stationary probability distribution and signal-to-noise ratio are discussed, respectively. Research results show that structure of stationary probability distribution transfers from extinction state to tumor stable one as k, s 1 , s 2 and s 3 increase; signal-to-noise ratio as a function of additive noise intensity exhibits maximum and minimum, maximum and minimum are the identifying characteristics of stochastic resonance and stochastic reverse-resonance phenomenon. However for the curve of signal-to-noise ratio as a function of multiplicative noise intensity, there exhibits only a maximum and increases of k, s 1 and s 3 weakens the stochastic resonance and stochastic reverse-resonance; conversely, increase of s 2 enhances stochastic resonance and stochastic reverse-resonance in tumor model under immune surveillance.

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“…Thus, quasistationary probability distribution (SPD) function P st ðx; tÞ can be derived from Eqs. (11) and (12) in the adiabatic limit as…”

Section: Stationary Properties Of Tumor Cell Growth Modelmentioning

confidence: 99%

“…The law of tumor cell growth has been investigated extensively [9][10][11]. Scientists are trying to find exact measures to control tumors and cure cancers and they have shown that there is an interesting and significant case for immunotherapy in tumor treatments [12,13].…”

Section: Introductionmentioning

confidence: 99%

Transition and resonance induced by colored noises in tumor model under immune surveillance

et al. 2014

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“…Study of systems driven by noise have been of growing interest in the last three decades, and stochastic approach is proving to be a reliable approach with its application cutting across many fields such as in biology, physics and chemistry. A more realistic approach to modeling biological systems driven by noise especially from external source formulated as Langevin equation is that involved colored effect, where the correlation at different times are not proportional to the delta function δ(t − t ) [1,2]. Systems driven by colored noise are non-Markovian, the underlying transition probability and does not satisfy the Fokker-Planck equation which is derived under the Markovian assumption.…”

Section: Introductionmentioning

confidence: 99%

Effect of tumor microenvironmental factors on the steady state of tumor growth with non-zero correlation time

Idris¹,

Bakar²

2016

ams

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The effect of non-immunogenic tumor microenvironmental factors on the steady state tumor growth dynamics modeled by multiplicative colored noise is investigated. Using the Novikov theorem and Fox approach, an approximate Fokker-Planck equation for the non-Markovian stochastic model is obtained and analytic expression for the steady state distribution P st (x) is derived. We find that the strength of the tumor response to the microenvironmental factors effect θ reduces the value of the steady state distribution P st (x) of tumor growth at weak correlation time τ which is an inhibitive effect, and at strong correlation time the inhibitive effect is suppressed and instead the value of the steady state distribution is increased which corresponds to growth enhancement. The result indicated that the growth effect exerted by the non-immunogenic tumor microenvironmental factors on tumor growth depend on the correlation time strength τ of the tumor response.

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Colored noises and time delay induced periodic square calcium wave

Duan

2014

Indian J Phys

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Effects of self-correlation time on stability of metastable state in logistic model

Cited by 5 publications

References 16 publications

Transition and resonance induced by colored noises in tumor model under immune surveillance

Transition and resonance induced by colored noises in tumor model under immune surveillance

Effect of tumor microenvironmental factors on the steady state of tumor growth with non-zero correlation time

Colored noises and time delay induced periodic square calcium wave

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