Blue Sky Catastrophe and FOLD-HOPF Bifuraction in Gavrilov-Shilnikov System Lenka Pribylova and Veronika Hajnova, Masaryk University, Brno, Czech Republic Animation of trajectories near Blue Sky Catastrophe in Gavrilov-Shilnikov System depending on parameters Sources: [1] Blue-sky catastrophe, Andrey Shilnikov and Dmitry Turaev (2007), Scholarpedia, 2(8):1889.
<Text-field style="Heading 1" layout="Heading 1">Code (run first)</Text-field> 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
Gavrilov-Shilnikov System LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzZaLUkjbWlHRiQ2JVEjZjFGJy8lJ2l0YWxpY0dRJXRydWVGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRictSSNtb0dGJDYtUSomY29sb25lcTtGJy9GM1Enbm9ybWFsRicvJSZmZW5jZUdRJmZhbHNlRicvJSpzZXBhcmF0b3JHRj0vJSlzdHJldGNoeUdGPS8lKnN5bW1ldHJpY0dGPS8lKGxhcmdlb3BHRj0vJS5tb3ZhYmxlbGltaXRzR0Y9LyUnYWNjZW50R0Y9LyUnbHNwYWNlR1EsMC4yNzc3Nzc4ZW1GJy8lJ3JzcGFjZUdGTC1JKG1mZW5jZWRHRiQ2JC1GIzYsLUYsNiVRInhGJ0YvRjItRjY2LVEiLEYnRjlGOy9GP0YxRkBGQkZERkZGSC9GS1EmMC4wZW1GJy9GTlEsMC4zMzMzMzMzZW1GJy1GLDYlUSJ5RidGL0YyRlctRiw2JVEiekYnRi9GMkZXLUYsNiVRI211RicvRjBGPUY5RlctRiw2JVEoZXBzaWxvbkYnRmJvRjlGOUY5LUY2Ni1RKCZzcmFycjtGJ0Y5RjtGPkZARkJGREZGRkhGZW4vRk5GZm5GVC1GNjYtUScmc2RvdDtGJ0Y5RjtGPkZARkJGREZGRkhGZW5GaW8tRlA2JC1GIzYqLUkjbW5HRiQ2JFEiMkYnRjktRjY2LVEiK0YnRjlGO0Y+RkBGQkZERkZGSC9GS1EsMC4yMjIyMjIyZW1GJy9GTkZpcEZfby1GNjYtUSgmbWludXM7RidGOUY7Rj5GQEZCRkRGRkZIRmhwRmpwLUZicDYkUSMxMEYnRjlGam8tRlA2JC1GIzYmLUklbXN1cEdGJDYlRlQtRiM2JEZhcEY5LyUxc3VwZXJzY3JpcHRzaGlmdEdRIjBGJ0ZlcC1GZnE2JUZpbkZocUZqcUY5RjlGOUY5RmVwLUZmcTYlRlxvRmhxRmpxRmVwLUY2Ni1RIn5GJ0Y5RjtGPkZARkJGREZGRkhGZW5GaW9GXXJGZXBGYXBGam9GaW4tRjY2LVEiO0YnRjlGO0ZaRkBGQkZERkZGSEZlbkZNLUknbXNwYWNlR0YkNiYvJSdoZWlnaHRHUSYwLjBleEYnLyUmd2lkdGhHRmZuLyUmZGVwdGhHRlxzLyUqbGluZWJyZWFrR1EobmV3bGluZUYnLUZocjYmRmpyRl1zRl9zL0Zic1ElYXV0b0YnLUYsNiVRI2YyRidGL0YyRjVGT0Zmby1GNjYtUSomdW1pbnVzMDtGJ0Y5RjtGPkZARkJGREZGRkhGaHBGanAtRmZxNiVGXG8tRiM2JC1GYnA2JFEiM0YnRjlGOUZqcUZbcS1GUDYkLUYjNiYtRmJwNiRRIjFGJ0Y5RmVwRmluRjlGOUZqby1GUDYkLUYjNipGX3JGZXBGXXJGZXBGYXBGam9GaW5GOUY5RltxLUZicDYkUSI0RidGOUZqb0ZURmVwRl9vRmpvRmluRmRyRmFyRmdyRmRzLUYsNiVRI2YzRidGL0YyRjVGT0Zmb0ZldEZqb0ZfckZlcEZlcUZbcUZjb0ZkckZhci8lK2V4ZWN1dGFibGVHRj1GOQ== LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYnLUkjbWlHRiQ2JVEoZXBzaWxvbkYnLyUnaXRhbGljR1EmZmFsc2VGJy8lLG1hdGh2YXJpYW50R1Enbm9ybWFsRictSSNtb0dGJDYtUSomY29sb25lcTtGJ0YyLyUmZmVuY2VHRjEvJSpzZXBhcmF0b3JHRjEvJSlzdHJldGNoeUdGMS8lKnN5bW1ldHJpY0dGMS8lKGxhcmdlb3BHRjEvJS5tb3ZhYmxlbGltaXRzR0YxLyUnYWNjZW50R0YxLyUnbHNwYWNlR1EsMC4yNzc3Nzc4ZW1GJy8lJ3JzcGFjZUdGSS1JI21uR0YkNiRRIjBGJ0YyLyUrZXhlY3V0YWJsZUdGMUYy Verify 0 is an equillibrium. LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYnLUkjbWlHRiQ2JVEoY29udmVydEYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1JKG1mZW5jZWRHRiQ2JC1GIzYuLUY2NiQtRiM2KC1GLDYlUSNmMUYnRi9GMi1GNjYkLUYjNiwtSSNtbkdGJDYkUSIwRicvRjNRJ25vcm1hbEYnLUkjbW9HRiQ2LVEiLEYnRkkvJSZmZW5jZUdRJmZhbHNlRicvJSpzZXBhcmF0b3JHRjEvJSlzdHJldGNoeUdGUS8lKnN5bW1ldHJpY0dGUS8lKGxhcmdlb3BHRlEvJS5tb3ZhYmxlbGltaXRzR0ZRLyUnYWNjZW50R0ZRLyUnbHNwYWNlR1EmMC4wZW1GJy8lJ3JzcGFjZUdRLDAuMzMzMzMzM2VtRidGRUZLRkVGSy1GLDYlUSNtdUYnL0YwRlFGSUZLLUYsNiVRKGVwc2lsb25GJ0Zhb0ZJRklGSS1GTDYtUSI9RidGSUZPL0ZTRlFGVEZWRlhGWkZmbi9GaW5RLDAuMjc3Nzc3OGVtRicvRlxvRmpvRkUvJStleGVjdXRhYmxlR0ZRRklGSS1GTDYvUSRhbmRGJy8lJWJvbGRHRjEvRjNRJWJvbGRGJy8lK2ZvbnR3ZWlnaHRHRmRwRk9GaG9GVEZWRlhGWkZmbkZobi9GXG9Gam4tRjY2JC1GIzYoLUZMNi1RIn5GJ0ZJRk9GaG9GVEZWRlhGWkZmbkZobkZncC1GLDYlUSNmMkYnRi9GMkZBRmVvRkVGSUZJRl5wRlxxLUY2NiQtRiM2KC1GLDYlUSNmM0YnRi9GMi1GNjYkLUYjNi1GRUZLRkVGS0ZFRktGXm9GS0Zib0ZccEZJRklGZW9GRUZccEZJRklGSy1GTDYtUSInRidGSUZPRmhvRlRGVkZYRlpGZm4vRmluUSwwLjExMTExMTFlbUYnRmdwLUYsNiVRKnRydWVmYWxzZUYnRi9GMkZdckZccEZJRkktRkw2LVEiO0YnRklGT0ZSRlRGVkZYRlpGZm5GaG5GW3BGXHBGSQ== Verify Jacobian is in Jordan form, otherwise use transformation procedure: 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