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- W4313484448 abstract "The classical two-species non-linear Predator-Prey system, often used in population dynamics modeling, is expressed in terms of a single positive coupling parameter $lambda$. Based on standard logarithmic transformations, we derive a novel $lambda$-textit{invariant} Hamiltonian resulting in two coupled first-order ODEs for ``hybrid-species'', textit{albeit} with one being textit{linear}; we thus derive a new exact, closed-form, single quadrature solution valid for any value of $lambda$ and the system's energy. In the particular case $lambda = 1$ the ODE system completely uncouples and a new, exact, energy-only dependent simple quadrature solution is derived. In the case $lambda neq 1$ an accurate practical approximation uncoupling the non-linear system is proposed and solutions are provided in terms of explicit quadratures together with high energy asymptotic solutions. A novel, exact, closed-form expression of the system's oscillation period valid for any value of $lambda$ and orbital energy is also derived; two fundamental properties of the period are established; for $lambda = 1$ the period is expressed in terms of a universal energy function and shown to be the shortest." @default.
- W4313484448 created "2023-01-06" @default.
- W4313484448 creator A5016474872 @default.
- W4313484448 date "2022-12-29" @default.
- W4313484448 modified "2023-09-27" @default.
- W4313484448 title "Predator-Prey Linear Coupling with Hybrid Species" @default.
- W4313484448 doi "https://doi.org/10.48550/arxiv.2301.00673" @default.
- W4313484448 hasPublicationYear "2022" @default.
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