QSER DECOMPOSITION OF PREDATORPREY DYNAMICS: SEPARATING SOURCE FROM ENVIRONMENT
The 2nd International Conference on Modern Problems of Mathematics, Mechanics and Their Applications (MPMMA 2026), Baku, Azerbaycan, 23 - 25 Haziran 2026, ss.113-114, (Özet Bildiri)
- Yayın Türü: Bildiri / Özet Bildiri
- Doi Numarası: 10.58225/mpmma.2026.113
- Basıldığı Şehir: Baku
- Basıldığı Ülke: Azerbaycan
- Sayfa Sayıları: ss.113-114
- Açık Arşiv Koleksiyonu: AVESİS Açık Erişim Koleksiyonu
- İstanbul Ticaret Üniversitesi Adresli: Evet
Özet
The Lotka-Volterra predator-prey model is a cornerstone of mathematical ecology, yet it conflates intrinsic population dynamics with interaction effects. This paper applies the SourceEnvironment-Response (QSER) framework to separate these causally distinct components. We decompose each population as 𝑹 = 𝑺 − 𝑬, where S is the source field (what the population would do in isolation) and E is the environmental field (accumulated interaction history). For prey, 𝑆𝑥 = 𝑥0 𝑒 𝛼𝑡 (intrinsic exponential growth). For predators, (𝑆𝑦 = 𝑦0) (constant source predators have no intrinsic dynamics; their entire fluctuation is environmental). The environmental fields satisfy (𝐸̇ 𝑥 = 𝛼𝐸𝑥 + 𝛽𝑥𝑦 and 𝐸̇ 𝑦 = 𝛾𝑦 − 𝛿𝑥𝑦, with 𝐸𝑥(0) = 0, 𝐸𝑦(0) = 0. Four validity tests— source consistency, zero initial condition of E, exact reconstruction 𝑅 = 𝑆 − 𝐸 , and infinite memory of S —confirm the physical correctness of the split. Numerical results show that QSER matches the traditional method to machine precision (mean error 2.45 × 10−11 for prey, 9.18 × 10−12for predators). This reframing reveals that predator dynamics are purely environmental: they have no intrinsic source beyond their initial condition.