File:Lotka-Volterra orbits 01.svg

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Summary

Solutions of the Lotka-Volterra equations obtained by a fourth-order Runge-Kutta algorithm, for parameters <img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/e1ab1d44e6ccc10f965182d28785519c14977438" class="mwe-math-fallback-image-inline mw-math-element" aria-hidden="true" style="vertical-align: -0.838ex; width:8.126ex; height:2.843ex;" alt="{\displaystyle \alpha =2/3}">, <img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/c90ae99a8e23135fc8b91793c4820595846c0c86" class="mwe-math-fallback-image-inline mw-math-element" aria-hidden="true" style="vertical-align: -0.838ex; width:7.97ex; height:2.843ex;" alt="{\displaystyle \beta =4/3}">, <img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/5682ebb86d6f024a15f4a2c1c7cb08412720bcaf" class="mwe-math-fallback-image-inline mw-math-element" aria-hidden="true" style="vertical-align: -0.838ex; width:5.555ex; height:2.676ex;" alt="{\displaystyle \gamma =1}"> and <img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/30c5c1a63ccd876384e6cf0a31296e3aee31ac84" class="mwe-math-fallback-image-inline mw-math-element" aria-hidden="true" style="vertical-align: -0.338ex; width:5.341ex; height:2.343ex;" alt="{\displaystyle \delta =1}">. Initial conditions (circle symbols) vary from <img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/12fb1a4ae271b93c61fe117b691677bb27609f25" class="mwe-math-fallback-image-inline mw-math-element" aria-hidden="true" style="vertical-align: -0.338ex; width:3.003ex; height:2.176ex;" alt="{\displaystyle 0.9}"> to <img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/3fa83a10a5dac380c9d88f386849b45c5d65997e" class="mwe-math-fallback-image-inline mw-math-element" aria-hidden="true" style="vertical-align: -0.338ex; width:3.003ex; height:2.176ex;" alt="{\displaystyle 1.8}"> with <img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/2fd4ef2757b5bed78a9f074f2a9346ddacd135e4" class="mwe-math-fallback-image-inline mw-math-element" aria-hidden="true" style="vertical-align: -0.338ex; width:3.003ex; height:2.176ex;" alt="{\displaystyle 0.1}"> step.

Licensing

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File history

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Date/TimeThumbnailDimensionsUserComment
current23:55, 14 January 2017Thumbnail for version as of 23:55, 14 January 2017476 × 471 (968 KB)127.0.0.1 (talk)Solutions of the Lotka-Volterra equations obtained by a fourth-order Runge-Kutta algorithm, for parameters <span><span class="mwe-math-mathml-inline mwe-math-mathml-a11y mw-math-element" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow class="MJX-TeXAtom-ORD"><mstyle displaystyle="true" scriptlevel="0"><mi>α<!-- α --></mi><mo>=</mo><mn>2</mn><mrow class="MJX-TeXAtom-ORD"><mo>/</mo></mrow><mn>3</mn></mstyle></mrow><annotation encoding="application/x-tex">{\displaystyle \alpha =2/3}</annotation></semantics></math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/e1ab1d44e6ccc10f965182d28785519c14977438" class="mwe-math-fallback-image-inline mw-math-element" aria-hidden="true" style="vertical-align: -0.838ex; width:8.126ex; height:2.843ex;" alt="{\displaystyle \alpha =2/3}"></span>, <span><span class="mwe-math-mathml-inline mwe-math-mathml-a11y mw-math-element" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow class="MJX-TeXAtom-ORD"><mstyle displaystyle="true" scriptlevel="0"><mi>β<!-- β --></mi><mo>=</mo><mn>4</mn><mrow class="MJX-TeXAtom-ORD"><mo>/</mo></mrow><mn>3</mn></mstyle></mrow><annotation encoding="application/x-tex">{\displaystyle \beta =4/3}</annotation></semantics></math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/c90ae99a8e23135fc8b91793c4820595846c0c86" class="mwe-math-fallback-image-inline mw-math-element" aria-hidden="true" style="vertical-align: -0.838ex; width:7.97ex; height:2.843ex;" alt="{\displaystyle \beta =4/3}"></span>, <span><span class="mwe-math-mathml-inline mwe-math-mathml-a11y mw-math-element" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow class="MJX-TeXAtom-ORD"><mstyle displaystyle="true" scriptlevel="0"><mi>γ<!-- γ --></mi><mo>=</mo><mn>1</mn></mstyle></mrow><annotation encoding="application/x-tex">{\displaystyle \gamma =1}</annotation></semantics></math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/5682ebb86d6f024a15f4a2c1c7cb08412720bcaf" class="mwe-math-fallback-image-inline mw-math-element" aria-hidden="true" style="vertical-align: -0.838ex; width:5.555ex; height:2.676ex;" alt="{\displaystyle \gamma =1}"></span> and <span><span class="mwe-math-mathml-inline mwe-math-mathml-a11y mw-math-element" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow class="MJX-TeXAtom-ORD"><mstyle displaystyle="true" scriptlevel="0"><mi>δ<!-- δ --></mi><mo>=</mo><mn>1</mn></mstyle></mrow><annotation encoding="application/x-tex">{\displaystyle \delta =1}</annotation></semantics></math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/30c5c1a63ccd876384e6cf0a31296e3aee31ac84" class="mwe-math-fallback-image-inline mw-math-element" aria-hidden="true" style="vertical-align: -0.338ex; width:5.341ex; height:2.343ex;" alt="{\displaystyle \delta =1}"></span>. Initial conditions (circle symbols) vary from <span><span class="mwe-math-mathml-inline mwe-math-mathml-a11y mw-math-element" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow class="MJX-TeXAtom-ORD"><mstyle displaystyle="true" scriptlevel="0"><mn>0.9</mn></mstyle></mrow><annotation encoding="application/x-tex">{\displaystyle 0.9}</annotation></semantics></math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/12fb1a4ae271b93c61fe117b691677bb27609f25" class="mwe-math-fallback-image-inline mw-math-element" aria-hidden="true" style="vertical-align: -0.338ex; width:3.003ex; height:2.176ex;" alt="{\displaystyle 0.9}"></span> to <span><span class="mwe-math-mathml-inline mwe-math-mathml-a11y mw-math-element" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow class="MJX-TeXAtom-ORD"><mstyle displaystyle="true" scriptlevel="0"><mn>1.8</mn></mstyle></mrow><annotation encoding="application/x-tex">{\displaystyle 1.8}</annotation></semantics></math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/3fa83a10a5dac380c9d88f386849b45c5d65997e" class="mwe-math-fallback-image-inline mw-math-element" aria-hidden="true" style="vertical-align: -0.338ex; width:3.003ex; height:2.176ex;" alt="{\displaystyle 1.8}"></span> with <span><span class="mwe-math-mathml-inline mwe-math-mathml-a11y mw-math-element" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow class="MJX-TeXAtom-ORD"><mstyle displaystyle="true" scriptlevel="0"><mn>0.1</mn></mstyle></mrow><annotation encoding="application/x-tex">{\displaystyle 0.1}</annotation></semantics></math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/2fd4ef2757b5bed78a9f074f2a9346ddacd135e4" class="mwe-math-fallback-image-inline mw-math-element" aria-hidden="true" style="vertical-align: -0.338ex; width:3.003ex; height:2.176ex;" alt="{\displaystyle 0.1}"></span> step.
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