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Sains Malaysiana 55(8)(2026): 1249-1261
http://doi.org/10.17576/jsm-2026-5508-02
Pemodelan Lotka-Volterra Interaksi KDNK, PLA dan Harga
Minyak Menggunakan Kaedah Euler Tak Piawai
(Lotka-Volterra Modeling of the Interaction of GDP, PLA and
Oil Price Using Non-Standard Euler Method)
MOHAMMAD
KHATIM HASAN*, NOOR ASHIKIN OTHMAN & BAHARI IDRUS
Pusat Kajian Teknologi Kecerdasan Buatan,
Fakulti Teknologi dan Sains Maklumat, Universiti Kebangsaan Malaysia, 43600 UKM
Bangi, Selangor, Malaysia
Diserahkan: 31 Oktober 2025/Diterima: 28 Julai 2026
Abstrak
Hubungan yang rumit antara Keluaran Dalam Negara Kasar (KDNK),
Pelaburan Langsung Asing (PLA) dan Harga Minyak Mentah (HMM) adalah kunci untuk
memahami sistem ekonomi, kerana pemboleh ubah ini secara kolektif mempengaruhi
trajektori ekonomi nasional dan global. KDNK mencerminkan kesejahteraan ekonomi
dan keyakinan pelabur, PLA berperanan sebagai pemangkin pertumbuhan dengan
memperkenalkan modal dan teknologi, manakala HMM mempengaruhi kos pengeluaran, inflasi
dan kestabilan negara pengeksport dan pengimport minyak. Kajian ini memberi
tumpuan kepada Malaysia dengan hasil minyak dan PLA memainkan peranan penting
dalam membentuk prestasi ekonomi. Model tak linear berinspirasikan
Lotka-Volterra baharu dicadangkan untuk menggambarkan hubungan saling
kebergantungan antara KDNK, PLA dan HMM. Walau bagaimanapun, hasil ujian
kestabilan mendedahkan bahawa titik keseimbangan sistem adalah tidak stabil
dengan gangguan kecil mencetuskan dinamik berayun atau mencapah, mencerminkan
kerentanan Malaysia terhadap kitaran ekonomi dan kejutan luaran. Penemuan ini
menonjolkan hubungan dinamik antara pemboleh ubah tersebut serta
ketidakstabilan yang wujud dalam ekonomi bergantung kepada tenaga. Model yang
dicadangkan menawarkan pandangan kukuh terhadap hubungan tak linear antara
KDNK, PLA dan HMM, sekali gus menekankan keperluan untuk intervensi dasar yang
disasarkan bagi mengurangkan ketidakstabilan. Bagi memastikan ketepatan model
dan mengatasi masalah kestabilan, kami menghasilkan kaedah Euler tak piawai
(KETP), pendekatan berangka yang direka untuk mengekalkan sifat positif,
keterbatasan dan kestabilan dalam simulasi. Hasil kajian menunjukkan ketepatan
ramalan yang tinggi bagi KDNK dan PLA dengan nilai Peratusan Ralat Purata
Mutlak (PRPM) yang rendah serta ketepatan yang munasabah bagi HMM. Dengan
menyediakan kerangka ramalan, kajian ini melengkapkan pembuat dasar dan pelabur
dengan alat untuk mengemudi landskap ekonomi Malaysia yang berubah-ubah, sambil
menawarkan strategi untuk mengukuhkan daya tahan dan pertumbuhan mampan di
tengah-tengah ketidakpastian pasaran tenaga global.
Kata kunci: Dinamik Lotka-Volterra; interaksi
KDNK-PLA-HMM; kaedah Euler tak piawai (KETP); pemodelan harga minyak mentah;
sistem ekonomi tak linear
Abstract
The intricate interplay between Gross Domestic Product (GDP),
Foreign Direct Investment (FDI), and Crude Oil Prices (COP) forms the
cornerstone of understanding economic systems, as these variables collectively
shape national and global economic trajectories. GDP reflects economic
well-being and investor confidence, FDI serves as a growth catalyst by
introducing capital and technology, while COP influences production costs,
inflation, and the stability of oil-exporting and importing nations. This study
focuses on Malaysia, where oil revenues and FDI play pivotal roles in shaping
economic performance. A new Lotka-Volterra-inspired nonlinear model is proposed
to capture the interdependencies between GDP, FDI, and COP. However, stability
analysis shows that the system’s equilibrium points are unstable, with minor
disturbances triggering oscillatory or divergent dynamics, underscoring
Malaysia’s vulnerability to economic cycles and external shocks. These findings
highlight the dynamic relationships between these variables and the inherent
volatility in energy-dependent economies. The proposed model offers robust
insights into the nonlinear connections between GDP, FDI, and COP, emphasizing
the urgent need for targeted policy interventions to mitigate instability. To
ensure model accuracy and address stability challenges, we developed a
Nonstandard Euler Method (NSEM), a numerical approach designed to preserve
positivity, boundedness, and stability in simulations. The results demonstrate
high predictive accuracy for GDP and FDI, with low Mean Absolute Percentage
Error (MAPE) values, alongside reasonable accuracy for COP. By providing a
predictive framework, this study equips policymakers and investors with
essential tools to navigate Malaysia’s ever-evolving economic landscape,
offering strategies to bolster resilience and sustainable growth amidst global
energy market uncertainties.
Keywords: Crude oil price modelling; GDP-FDI-COP interactions;
Lotka-Volterra dynamics; nonlinear economic systems; nonstandard Euler method
(NSEM)
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*Pengarang untuk surat-menyurat;
email: mkh@ukm.edu.my
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