<p>In this paper we investigate the propagation dynamics of a Leslie–Gower predator–prey model with the classical Lotka–Volterra functional response in a shifting habitat. It is assumed that both the prey and the predator decline near negative infinity and grow near positive infinity. We first obtain the spreading properties of the system. More specifically, the persistence and extinction of the predator depend on the speed of the shifting environment <i>c</i> and the invasion speed of the predator <InlineEquation ID="IEq1"> <EquationSource Format="TEX">$\mu ^{*}(\infty )=2\sqrt{d_{2}r_{2}(\infty )}$</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <msup> <mi>μ</mi> <mrow> <mrow /> <mo>∗</mo> </mrow> </msup> <mrow> <mo stretchy="false">(</mo> <mi>∞</mi> <mo stretchy="false">)</mo> </mrow> <mo>=</mo> <mn>2</mn> <msqrt> <mrow> <msub> <mi>d</mi> <mn>2</mn> </msub> <msub> <mi>r</mi> <mn>2</mn> </msub> <mrow> <mo stretchy="false">(</mo> <mi>∞</mi> <mo stretchy="false">)</mo> </mrow> </mrow> </msqrt> </mrow> </math></EquationSource> </InlineEquation> in the favorite environment. Then, we show the existence of forced KPP waves with the forced speed <InlineEquation ID="IEq2"> <EquationSource Format="TEX">$c>0$</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi>c</mi> <mo>></mo> <mn>0</mn> </mrow> </math></EquationSource> </InlineEquation> connecting the trivial state to the co-existence equilibrium and the existence and nonexistence of the mixed front-pulse-type forced waves. Finally, we parameterize the model by using real ecological data and analyze the population dynamics: (a) the Davis Strait polar bears and harp seals and (b) white-tailed deer and blacklegged ticks in Texas, over the coming decades.</p>

Propagation Dynamics of a Leslie–Gower Prey–Predator Model in a Shifting Habitat

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发表日期：

2026年4月13日

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Yaqian Xu,
Zhi-Cheng Wang

摘要

In this paper we investigate the propagation dynamics of a Leslie–Gower predator–prey model with the classical Lotka–Volterra functional response in a shifting habitat. It is assumed that both the prey and the predator decline near negative infinity and grow near positive infinity. We first obtain the spreading properties of the system. More specifically, the persistence and extinction of the predator depend on the speed of the shifting environment c and the invasion speed of the predator $\mu ^{*}(\infty )=2\sqrt{d_{2}r_{2}(\infty )}$ $μ^{*} (\infty) = 2 \sqrt{d_{2} r_{2} (\infty)}$ in the favorite environment. Then, we show the existence of forced KPP waves with the forced speed $c>0$ $c > 0$ connecting the trivial state to the co-existence equilibrium and the existence and nonexistence of the mixed front-pulse-type forced waves. Finally, we parameterize the model by using real ecological data and analyze the population dynamics: (a) the Davis Strait polar bears and harp seals and (b) white-tailed deer and blacklegged ticks in Texas, over the coming decades.