Analisis Dinamik Model Logistik Diskrit Nonlinier Berbasis Simulasi Komputasi dan Bifurkasi
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Haves Qausar
*
Universitas Malikussaleh, Aceh Utara,
Indonesia
https://orcid.org/0000-0001-6306-2688
- Zata Hasyyati Universitas Malikussaleh, Aceh Utara, Indonesia (*) Corresponding Author
Abstract
The discrete logistic model is a simple nonlinear model capable of producing stable, periodic, and chaotic dynamics; however, chaos identification is often based only on orbit visualisation or bifurcation diagrams. This study aims to analyse its dynamics using analytical results and computational indicators. This study applies mathematical modelling and computational simulation; therefore, it involves neither respondents nor a field research location. The model was analysed using the control parameter , which determines changes in the system dynamics, from to , an initial value of , iterations, and removal of the first iterations as the transient phase. The techniques comprised local stability analysis, time-series simulation, bifurcation diagrams, Lyapunov exponents, and sensitivity to initial conditions. Results show that the zero fixed point is stable for , the nonzero fixed point is stable for , and the first bifurcation occurs at . Period-2, period-4, and period-8 orbits emerge at , , and , respectively. At , the Lyapunov exponent is , and two orbits with an initial difference of diverge, supporting chaotic dynamics. Conversely, at , a period-3 orbit emerges with a Lyapunov exponent of as a periodic window. This study provides a systematic and reproducible computational evaluation framework for nonlinear discrete dynamics.
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