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Obtaining an analytical representation of the solutions of nonlinear differential equations has been a challenge for many years. This difficulty is particularly pronounced when these equations model a physical phenomenon, which makes the exact solution even more difficult to find. In this paper, we present a global semi-analytical approach for deriving global rational approximants to Riccati equations and logistic growth models, which are commonly employed in the modeling of complex systems. We also show that our approach can be efficiently used to solve a system of nonlinear equations that represent a dynamical system without closed solution, namely the drug consumption model. This current global semi-analytical method consists firstly in generating the solutions of these nonlinear differential equations in terms of series expansions for small and large values. Then, two-point Padé approximants are applied to provide global approximate representation solutions that agree with the exact solution over the whole period of time. To demonstrate the effectiveness of our study, some examples given in the literature have been solved using our approach. Numerical comparisons between the present approach and other methods are also included. • Propose an efficient and accurate approach for solving Riccati differential equations and logistic growth models and drug consumption model. • Provide the series expansions for small and large values to the solution of the equations. • Provide a global solution in terms of a rational function using both series expansions of small and large values. • Numerical examples were given to show the accuracy and performance of the proposed approach. [ABSTRACT FROM AUTHOR]

In this paper, we study the role of autophagy in yeast cell population dynamics in response to starvation by a mathematical model based on the logistic growth model. We analytically study the boundedness of solutions, and the existence and stability of equilibrium states under general biologically acceptable assumptions. Finally, we perform numerical studies for Saccharomyces cerevisiae response to starvation with autophagy. The results show that autophagy is valuable in maintaining cell population in starvation, and attenuating population fluctuations in response to perturbations in environmental nutrients. Furthermore, we show that proper level autophagy promotes cell survival through the inhibition of cell death by autophagy as well as the secretion of nutrients from autophagic cells, however excessive autophagy can decrease cell population due to autophagic cell death. [ABSTRACT FROM AUTHOR]