Dynamical properties of a logistic growth model with cross-correlated noises

Cheng-Yu, Wang; Gao, Yun; Wang, Xuewen; Song, Yong; Zhou, Peng; Yan, Hai

doi:10.1016/j.physa.2010.03.053

Cited by 13 publications

(3 citation statements)

References 23 publications

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“…Nutrient accumulation in the above ground biomass of P . pinnata was described using the logistic equation W = a /[1 + exp (b − ct) ] [ 43 ], where W is the nutrient accumulation variable at days after emergence t , and a , b , c are values calculated using the SAS software. Plant growth, growth rates, and growth acceleration curves were obtained using the first, second and third derivatives of this logistic equation.…”

Section: Methodsmentioning

confidence: 99%

Pseudomonas aeruginosa RRALC3 Enhances the Biomass, Nutrient and Carbon Contents of Pongamia pinnata Seedlings in Degraded Forest Soil

et al. 2015

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The study was aimed at assessing the effects of indigenous Plant Growth Promoting Bacterium (PGPB) on the legume Pongamia pinnata in the degraded soil of the Nanmangalam Reserve Forest (NRF) under nursery conditions. In total, 160 diazotrophs were isolated from three different nitrogen-free semi-solid media (LGI, Nfb, and JMV). Amongst these isolates, Pseudomonas aeruginosa RRALC3 exhibited the maximum ammonia production and hence was selected for further studies. RRALC3 was found to possess multiple plant growth promoting traits such as nitrogen accumulation (120.6ppm); it yielded a positive amplicon with nifH specific primers, tested positive for Indole Acetic Acid (IAA; 18.3μg/ml) and siderophore production, tested negative for HCN production and was observed to promote solubilization of phosphate, silicate and zinc in the plate assay. The 16S rDNA sequence of RRALC3 exhibited 99% sequence similarity to Pseudomonas aeruginosa JCM5962. Absence of virulence genes and non-hemolytic activity indicated that RRALC3 is unlikely to be a human pathogen. When the effects of RRALC3 on promotion of plant growth was tested in Pongamia pinnata, it was observed that in Pongamia seedlings treated with a combination of RRALC3 and chemical fertilizer, the dry matter increased by 30.75%. Nitrogen, phosphorus and potassium uptake increased by 34.1%, 27.08%, and 31.84%, respectively, when compared to control. Significant enhancement of total sugar, amino acids and organic acids content, by 23.4%, 29.39%, and 26.53% respectively, was seen in the root exudates of P. pinnata. The carbon content appreciated by 4-fold, when fertilized seedlings were treated with RRALC3. From the logistic equation, the rapid C accumulation time of Pongamia was computed as 43 days longer than the control when a combination of native PGPB and inorganic fertilizer was applied. The rapid accumulation time of N, P and K in Pongamia when treated with the same combination as above was 15, 40 and 33 days longer, respectively, as compared to the control.

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Section: Methodsmentioning

confidence: 99%

Pseudomonas aeruginosa RRALC3 Enhances the Biomass, Nutrient and Carbon Contents of Pongamia pinnata Seedlings in Degraded Forest Soil

et al. 2015

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“…Many researchers have extended the logistic model to include perturbations in the model parameters for feedback by periodic or random modulation (e.g. [4,5,6,7,8,9,10,11]) or to couple to the evolution of other systems (e.g. [12]).…”

Section: Introductionmentioning

confidence: 99%

Sustainable theory of a logistic model - Fisher information approach

Al-Saffar

Kim

2017

Mathematical Biosciences

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Abstract. Information theory provides a useful tool to understand the evolution of complex nonlinear systems and their sustainability. In particular, Fisher Information (FI) has been evoked as a useful measure of sustainability and the variability of dynamical systems including self-organising systems. By utilising FI, we investigate the sustainability of the logistic model for different perturbations in the positive and/or negative feedback. Specifically, we consider different oscillatory modulations in the parameters for positive and negative feedbacks and investigate their effect on the evolution of the system and Probability Density Functions (PDFs). Depending on the relative time scale of the perturbation to the response time of the system (the linear growth rate), we demonstrate the maintenance of the initial condition for a long time, manifested by a broad bimodal PDF. We present the analysis of FI in different cases and elucidate its implications for the sustainability of population dynamics. We also show that a purely oscillatory growth rate can lead to a finite amplitude solution while self-organisation of these systems can break down with an exponentially growing solution due to the fluctuation in negative feedback.

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“…However, to the leading order in the correlation time, an approximate approach to the Markovian Fokker-Planck equation can be found [3,4]. The study of complex biological and physical systems driven by colored noise have been given much attention in the recent decades [5][6][7][8][9]. Moreover, Transitions in a logistic growth model induced by noise coupling and noise color shows some interesting behavior [10].…”

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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Dynamical properties of a logistic growth model with cross-correlated noises

Cited by 13 publications

References 23 publications

Pseudomonas aeruginosa RRALC3 Enhances the Biomass, Nutrient and Carbon Contents of Pongamia pinnata Seedlings in Degraded Forest Soil

Pseudomonas aeruginosa RRALC3 Enhances the Biomass, Nutrient and Carbon Contents of Pongamia pinnata Seedlings in Degraded Forest Soil

Sustainable theory of a logistic model - Fisher information approach

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

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