In this paper, we present a generalization of the commonly used growth models. We introduce Koya-Goshu biological growth model, as a more general solution of the rate-state ordinary differential equation. It is shown ...In this paper, we present a generalization of the commonly used growth models. We introduce Koya-Goshu biological growth model, as a more general solution of the rate-state ordinary differential equation. It is shown that the commonly used growth models such as Brody, Von Bertalanffy, Richards, Weibull, Monomolecular, Mitscherlich, Gompertz, Logistic, and generalized Logistic functions are its special cases. We have constructed growth and relative growth functions as solutions of the rate-state equation. The generalized growth function is the most flexible so that it can be useful in model selection problems. It is also capable of generating new useful models that have never been used so far. The function incorporates two parameters with one influencing growth pattern and the other influencing asymptotic behaviors. The relationships among these growth models are studies in details and provided in a flow chart.展开更多
The current study investigates the predator-prey problem with assumptions that interaction of predation has a little or no effect on prey population growth and the prey’s grow rate is time dependent. The prey is assu...The current study investigates the predator-prey problem with assumptions that interaction of predation has a little or no effect on prey population growth and the prey’s grow rate is time dependent. The prey is assumed to follow the Gompertz growth model and the respective predator growth function is constructed by solving ordinary differential equations. The results show that the predator population model is found to be a function of the well known exponential integral function. The solution is also given in Taylor’s series. Simulation study shows that the predator population size eventually converges either to a finite positive limit or zero or diverges to positive infinity. Under certain conditions, the predator population converges to the asymptotic limit of the prey model. More results are included in the paper.展开更多
文摘In this paper, we present a generalization of the commonly used growth models. We introduce Koya-Goshu biological growth model, as a more general solution of the rate-state ordinary differential equation. It is shown that the commonly used growth models such as Brody, Von Bertalanffy, Richards, Weibull, Monomolecular, Mitscherlich, Gompertz, Logistic, and generalized Logistic functions are its special cases. We have constructed growth and relative growth functions as solutions of the rate-state equation. The generalized growth function is the most flexible so that it can be useful in model selection problems. It is also capable of generating new useful models that have never been used so far. The function incorporates two parameters with one influencing growth pattern and the other influencing asymptotic behaviors. The relationships among these growth models are studies in details and provided in a flow chart.
文摘The current study investigates the predator-prey problem with assumptions that interaction of predation has a little or no effect on prey population growth and the prey’s grow rate is time dependent. The prey is assumed to follow the Gompertz growth model and the respective predator growth function is constructed by solving ordinary differential equations. The results show that the predator population model is found to be a function of the well known exponential integral function. The solution is also given in Taylor’s series. Simulation study shows that the predator population size eventually converges either to a finite positive limit or zero or diverges to positive infinity. Under certain conditions, the predator population converges to the asymptotic limit of the prey model. More results are included in the paper.
文摘本研究通过对2022、2023年在黄河干流甘肃、宁夏段采集的274个硬刺高原鳅样本进行分析,旨在深入理解其生长特性,并丰富硬刺高原鳅的生物学研究内容。研究采用Von Bertalanffy生长方程(VBGF)、逻辑斯谛生长方程(Logistic GF)、Gompertz生长方程和幂指数生长方程对样本进行生长模拟,使用最大似然法估算模型参数,并依据AIC准则(Akaike Information Criterion)评估各模型的拟合效果,选择最佳模型,分析硬刺高原鳅的年龄组成及其生长特性。结果显示,VBGF生长方程(AIC值:63.74)为硬刺高原鳅的最适生长模型,其次为Gompertz生长方程(AIC值:64.11)、幂指数生长方程(AIC值:64.12),拟合效果最差的为Logistic生长方程(AIC值:65.05),其中硬刺高原鳅全长VBGF生长方程为:L_(t)=28.986·[1-e^(-0.097·(t_(1)+1.258))];体质量生长方程为:W_(t)=194.721·[1-e^(-0.097·(t_(1)+1.258))]^(2.9889)。研究结果可为硬刺高原鳅资源保护提供科学依据。
