{"id":24592258,"url":"https://github.com/yapeansa/competitive_species","last_synced_at":"2026-05-01T06:32:49.641Z","repository":{"id":273511778,"uuid":"919959099","full_name":"yapeansa/competitive_species","owner":"yapeansa","description":"Espécies competindo por um mesmo suprimento de alimento, sendo uma delas mais forte que a outra.","archived":false,"fork":false,"pushed_at":"2025-01-29T11:20:38.000Z","size":635,"stargazers_count":0,"open_issues_count":0,"forks_count":0,"subscribers_count":1,"default_branch":"main","last_synced_at":"2025-05-30T20:48:57.176Z","etag":null,"topics":["biology","computational-modeling","ecology","python"],"latest_commit_sha":null,"homepage":"","language":"Jupyter Notebook","has_issues":true,"has_wiki":null,"has_pages":null,"mirror_url":null,"source_name":null,"license":null,"status":null,"scm":"git","pull_requests_enabled":true,"icon_url":"https://github.com/yapeansa.png","metadata":{"files":{"readme":"README.md","changelog":null,"contributing":null,"funding":null,"license":null,"code_of_conduct":null,"threat_model":null,"audit":null,"citation":null,"codeowners":null,"security":null,"support":null,"governance":null,"roadmap":null,"authors":null,"dei":null,"publiccode":null,"codemeta":null}},"created_at":"2025-01-21T10:13:27.000Z","updated_at":"2025-01-29T11:20:42.000Z","dependencies_parsed_at":"2025-03-18T23:15:49.086Z","dependency_job_id":null,"html_url":"https://github.com/yapeansa/competitive_species","commit_stats":null,"previous_names":["yapeansa/competing_species","yapeansa/competitive_species"],"tags_count":0,"template":false,"template_full_name":null,"purl":"pkg:github/yapeansa/competitive_species","repository_url":"https://repos.ecosyste.ms/api/v1/hosts/GitHub/repositories/yapeansa%2Fcompetitive_species","tags_url":"https://repos.ecosyste.ms/api/v1/hosts/GitHub/repositories/yapeansa%2Fcompetitive_species/tags","releases_url":"https://repos.ecosyste.ms/api/v1/hosts/GitHub/repositories/yapeansa%2Fcompetitive_species/releases","manifests_url":"https://repos.ecosyste.ms/api/v1/hosts/GitHub/repositories/yapeansa%2Fcompetitive_species/manifests","owner_url":"https://repos.ecosyste.ms/api/v1/hosts/GitHub/owners/yapeansa","download_url":"https://codeload.github.com/yapeansa/competitive_species/tar.gz/refs/heads/main","sbom_url":"https://repos.ecosyste.ms/api/v1/hosts/GitHub/repositories/yapeansa%2Fcompetitive_species/sbom","scorecard":null,"host":{"name":"GitHub","url":"https://github.com","kind":"github","repositories_count":286080680,"owners_count":32487401,"icon_url":"https://github.com/github.png","version":null,"created_at":"2022-05-30T11:31:42.601Z","updated_at":"2026-04-30T13:12:12.517Z","status":"online","status_checked_at":"2026-05-01T02:00:05.856Z","response_time":64,"last_error":null,"robots_txt_status":"success","robots_txt_updated_at":"2025-07-24T06:49:26.215Z","robots_txt_url":"https://github.com/robots.txt","online":true,"can_crawl_api":true,"host_url":"https://repos.ecosyste.ms/api/v1/hosts/GitHub","repositories_url":"https://repos.ecosyste.ms/api/v1/hosts/GitHub/repositories","repository_names_url":"https://repos.ecosyste.ms/api/v1/hosts/GitHub/repository_names","owners_url":"https://repos.ecosyste.ms/api/v1/hosts/GitHub/owners"}},"keywords":["biology","computational-modeling","ecology","python"],"created_at":"2025-01-24T10:14:02.283Z","updated_at":"2026-05-01T06:32:49.625Z","avatar_url":"https://github.com/yapeansa.png","language":"Jupyter Notebook","funding_links":[],"categories":[],"sub_categories":[],"readme":"# Espécies em Competição\n\nDuas espécies competindo por um mesmo suprimento de alimento. Uma é mais forte que a outra.\n\n```math\n\\begin{align}\n    \u0026x' = x\\,(3 - 2\\,x - 2\\,y), \\\\\n    \u0026y' = y\\,(2 - x - y).\n\\end{align}\n```\n\n## Análise Qualitativa\n\n### Determinando as x-nullclines\n\nAs x-nullclines são os pontos do plano em que $x\\\\,(3 - 2\\\\,x - 2\\\\,y) = 0$, isto é, as x-nullclines são: $x = 0$ e $2\\\\,y = 3 - 2\\\\,x$.\n\n### Determinando as y-nullclines\n\nAs y-nullclines são os pontos do plano em que $y\\\\,(2 - x - y) = 0$. Assim, as y-nullclines são dadas por: $y = 0$ e $y = 2 - x$.\n\n### Pontos de equilíbrio\n\nOs pontos de equilíbrio são determinados pelas interseções das x-nullclines com as y-nullclines. Observamos que as retas $2\\\\,y = 3 - 2\\\\,x$ e $y = 2 - x$ são paralelas e portanto não se intersectam. Assim, temos os seguintes pontos de equilíbrio: $(0, 0), (0, 2), \\left(\\frac{3}{2}, 0\\right)$.\n\n### Retrato de fase\n\nDe posse das nullclines e dos pontos de equilíbrio, somos capazes de esboçar o retrato de fase do sistema. Abaixo apresentamos esse esboço com juntamente com os pontos de equilíbrio e as nullclines:\n\n\u003cdiv align=\"center\"\u003e\n    \u003cimg src=\"./src/retrato_de_fase.png\" alt=\"Retrato de Fase\"/\u003e\n\u003c/div\u003e\n\n### Linearização\n\nA matriz jacobiana para o sistema é a matriz $A$ dada por:\n\n```math\n    A = \\begin{pmatrix}\n        3 - 4\\,x - 2\\,y \u0026 - 2\\,x \\\\ - y \u0026 2 - x - 2\\,y\n    \\end{pmatrix}\n```\nDesta forma, o sistema linearizado na origem $(0,0)$ é dado por:\n```math\n\\begin{pmatrix} u' \\\\ v' \\end{pmatrix} = \n\\begin{pmatrix} 3 \u0026 0 \\\\ 0 \u0026 2 \\end{pmatrix}\\,\\begin{pmatrix} u \\\\ v \\end{pmatrix} = B\\,\\begin{pmatrix} u \\\\ v \\end{pmatrix}\n```\nPodemos observado que a matriz $B$ possui os autovalores $\\lambda_1 = 3$ e $\\lambda_2 = 2$. Como ambos os autovalores são positivos, o sistema não é hiperbólico e a solução do sistema linearizado próximo da origem descreve qualitativamente o sistema original. Portanto, o ponto de equilíbrio $(0, 0)$ é do tipo fonte. Assim, as soluções se afastam deste ponto ao longo do tempo.\n","project_url":"https://awesome.ecosyste.ms/api/v1/projects/github.com%2Fyapeansa%2Fcompetitive_species","html_url":"https://awesome.ecosyste.ms/projects/github.com%2Fyapeansa%2Fcompetitive_species","lists_url":"https://awesome.ecosyste.ms/api/v1/projects/github.com%2Fyapeansa%2Fcompetitive_species/lists"}