Sustainable theory of a logistic model - Fisher information approach

Abstract

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.

Fisher information approach to understand the Gompertz model

“…In the case of a periodic fluctuation D 0 sin(ωt), is included in the different model parameters, where D 0 and ω are the amplitude and frequency of the modulation, respectively. As in the Logistic equation in [1], the value of the amplitude is fixed to be D 0 = 7, to explore the influence of different values of ω and x 0 on the response of the Gompertz model. Specifically, it may be beneficial to study three different cases of the Gompertz model.…”

Ecological Implications of the Dynamics of Water Volume Growth in a Reservoir

“…The higher the r value, the greater the speed of the reservoir to reach saturation. This shows that the dynamic model of biotic population growth [Jorgensen, 1994;Peleg, 2006;Al-Saffar and Kim, 2017;Jin et al, 2018;Batista, 2020;Torrealba-Rodriguez et al, 2020] can be developed as a dynamics model of a-biotic population growth (water volume). The reproduction rate in a biotic population is defined by the rate of increase in the a-biotic population.…”

“…Eq. ( 1) is a population growth model that depends on the carrying capacity of the environment [Jorgensen, 1994;Kribs-Zaleta, 2004;Chong et al, 2005;Peleg et al, 2007;Pinol and Banzon, 2011;Al-Saffar and Kim, 2017]. Some of the dynamic models that are modified from Eq.…”

Global Stability for a Semidiscrete Logistic System with Feedback Control

“…During the last years, many scholars did works on the continuous time Logistic model and related system with feedback controls (see, e.g., [16][17][18][19][20][21][22] and references cited therein). In 1992, Gopalsamy introduced a certain differential equation as a feedback control variable into the logistic models and discussed the asymptotic behavior of solutions for the model with feedback controls [16].…”