**KATEGORI : Publikasi Ilmiah**

# The existence of Neimark-Sacker bifurcation on a discrete-time SIS-Epidemic model incorporating logistic growth and allee effect

**Authors**: Amelia Tri Rahma Sidik, Hasan S. Panigoro, Resmawan Resmawan, Emli Rahmi

In this article, the dynamical properties of a discrete-time SIS-Epidemic model incorporating logistic growth rate and Allee effect are investigated. The forward Euler discretization method is employed to obtain the discrete-time model. All possible fixed points are identified, including their local dynamics and the existence of two important phenomena, namely transcritical and period-doubling bifurcation. Some numerical simulations are explored to show the analytical findings, such as bifurcation diagrams, phase portraits, and time series. The occurrence of a period-3 window is shown numerically, which routes to chaotic solutions.

# Bifurcation Analysis of a Predator-Prey Model Involving Age Structure, Intraspecific Competition, Michaelis-Menten Type Harvesting, and Memory Effect

**Authors:** *HS Panigoro, E Rahmi, R Resmawan*

*The complexity of the dynamical behaviors of interaction between prey and its predator is studied. The prey and predator relationship involves the age structure and intraspecific competition on predators, and the nonlinear harvesting of prey following the Michaelis-Menten type term. Some biological validities are shown for the constructed model such as the existence and uniqueness as well as the non-negativity and boundedness of solutions. Three equilibrium points namely the origin, axial, and interior point are found including their global dynamics by employing the Lyapunov function along with the generalized Lassale invariant principle. The changes in dynamical behaviors driven by the harvesting and the memory effect are exhibited namely transcritical, saddle-node, backward, and Hopf bifurcations. The appearance of these interesting phenomena is strengthened by giving numerical simulations consisting of bifurcation diagrams, phase portraits, and their time series.*

Frontiers in Applied Mathematics and Statistics, 124, 2022

# DYNAMIC ANALYSIS OF THE MATHEMATICAL MODEL OF THE SPREAD OF CHOLERA WITH VACCINATION STRATEGIES

Authors: Nur Safitri Abdul, Lailany Yahya, R Resmawan, Agusyarif Rezka Nuha

This research discusses the math model of spreading cholera disease with a mathematical strategy of math model constructed by considering a vaccination strategy. In addition, there is a population of hyper infectious and less infectious bacteria so the model of SVIR-BhiBli type, by. The model is formed in the form of determination of fixed point, determination of basic reproductions numbers, analyzing the equilibrium point and sensitivity analysis. The equilibrium analysis produces two equilibrium points of a immediate-free equilibrium point of aceletotic local if and endemic equilibrium points will be stable local asymptotics if . Furthermore, numerical simulation that the increase in vaccination rate influences on the decline in value while increased rate of vaccine depreciation can increase the value of . In addition, sensitivity analysis shows that if the parameter is enhanced while other contrast parameters will contribute to the increase in value, as a result can increase the rate of transmission of cholera disease. Whereas if the parameter is enhanced while other contrast parameters will contribute to the decrease in value, as a result of the dissemination of the disease can be pressed very significantly.

Published in Barekeng (SINTA 2)

# GOODWIN MODEL WITH CLUSTERING WORKERS' SKILLS IN INDONESIAN ECONOMIC CYCLE

Authors: Sri Lestari Mahmud, Resmawan Resmawan, Sumarno Ismail, Nurwan Nurwan, Febriani Taki

The economic model which deals with the economic cycle is Goodwin's Model. It presents the relationship between the employment rate and wage shares. In this study, the modification model was made, taking into three types of workers, namely high, medium, and low-skilled workers. Studies of the model are conducted by determining the equilibrium point and its stability analysis. Furthermore, a numerical simulation is given to see which model satisfies the ideal of Goodwin‘s model cycle prediction by using Indonesian data from 2000 to 2020. In the end, an investigation into the effects of reducing the wage gap between the three types of workers was conducted. The results showed two equilibrium points, namely The Equilibrium Point without Employment Rate and The Wages Share (T1) and the Existence Equilibrium Point of Employment Rate and Wages Share (T2). T1 achieves a stable node condition when ScQ<d+pi+et while T2 reaches a stable center condition when ScQ>d+pi+et. The simulation showed Goodwin's model of high- and low-skilled workers produced the ideal of Goodwin model cycle predictions, whereas Goodwin's model of medium-skilled workers and the entire economy (capitalist) didn’t produce the ideal of Goodwin model cycle predictions. Eventually, the effects of reducing the wage gap make the economy unstable.

Published in Cauchy (SINTA 2)

# A discrete-time fractional-order Rosenzweig-Macarthur predator-prey model involving prey refuge

*Author: Hasan S. Panigoro, Emli Rahmi, Novianita Achmad, Sri Lestari Mahmud, R. Resmawan, Agusyarif Rezka Nuha*

In this article, the dynamical behaviors of a discrete-time fractional-order Rosenzweig-MacArthur model with prey refuge are studied. The piecewise constant arguments scheme is applied to obtain the discrete-time model. All possible fixed points and their existence conditions are investigated as well as the local behavior of nearby solutions in various contingencies. Numerical simulations such as the time series, phase portraits, and bifurcation diagrams are portrayed. Three types of bifurcations are shown numerically namely the forward, the period-doubling, and Neimark-Sacker bifurcations. Some phase portraits are depicted to justify the occurrence of those bifurcations.

Published in Communications in Mathematical Biology and Neuroscience (Q3)

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