Global Stability Analysis of a General Scalar Difference Equation

Abstract

We consider a general …rst order scalar di¤erence equation with and without Allee e¤ect. The model without Allee e¤ect represents asexual reproduction of a species while the model including Allee e¤ect represents sexual reproduction. We analyze global stabilities of both models analytically and compare the results obtained. Numerical simulations are included to support the analytical results. We conclude that Allee e¤ect decreases global stability of a nonnegative …xed point of the model. This result is di¤erent from the local stability behavior of the same …xed point of the model.

Global stability and bifurcation analysis of a discrete time SIR epidemic model

“…When the size of population is rarely small or the population has no overlapping generation, the discrete-time models are more appropriate than the continuous ones. In reality, most fish and insect populations have no overlap between successive generations, and thus their population evolves in discrete-time steps [1], [13], [17]. In theory, discrete-time system has much more richer dynamical behaviors than the continuous system.…”

Dynamics of a Prey-Predator System with Harvesting Effect on Prey

“…However, in ecology, populations evolve in discrete time steps, as there is no overlap between successive generations. It is therefore benefical to use difference equations (Ak Gümüş 2014;Gümüş and Kose 2012;Gümüş et al 2022b,c;Merdan and Gümüş 2012;Merdan et al 2018) or discrete-time systems involving prey-predator models (Danca et al 2019;Elsadany et al 2012;Gümüş 2020;Liu and Xiao 2007;Rana 2015), host-parasitoid models (Gümüş 2015;Gümüş and Kangalgil 2015;Gümüs et al 2020), epidemic models (Gümüş et al 2022a(Gümüş et al , 2019, and also fractional models (Selvam et al 2020;Singh et al 2019).…”

Bifurcation and Stability Analysis of a Discrete Time Sir Epidemic Model with Vaccination

“…Most of the biological occurrences in nature are illustrated by discrete time, which point to, that there are particular time instants at which the basic events in the system can occur, and it is not essential that at these discrete time instants only a exclusive event happens. The most realistic approach to non-overlapping generations like fish or insect populations, is created with discrete time system ( [6], [9], [15], [16], [17], [18]).…”