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New Insights into a Caputo Fractional-Order Lorenz-like System
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DOI：10.3390/fractalfract10080544.png)
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Abstract
En 中文
The present study is concerned with heteroclinic trajectories of a Caputo fractional-order Lorenz-type model ( 0 < α ≤ 1 ), a problem that has remained unresolved. Building upon previously known findings, we initially deduce two asymmetric heteroclinic connections that link the globally attracting equilibrium E 0 , the repelling equilibrium E + (or E − ), and the globally attracting equilibrium E − (or E + ), where E 0 = ( 0 , 0 , 0 ) and E ± = ( b d ± b 2 d 2 + 4 b c 2 , b d ± b 2 d 2 + 4 b c 2 , c + d ( b d ± b 2 d 2 + 4 b c 2 ) ) . Additionally, a novel heteroclinic trajectory is identified for two separate regimes: (1) joining the repelling E 0 with the globally attracting E + ( E − , respectively), alongside a locally attracting E − ( E + , respectively); (2) joining the repelling E − ( E + , respectively) with the globally attracting E + ( E − , respectively), alongside a locally attracting E 0 . All analytical claims are supported by numerical experiments.
Keywords:
Caputo fractional-order Lorenz-like system
heteroclinic orbit
Lyapunov function
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