2016 **Abstract:** We devote to studying the problem for the existence of homoclinic and heteroclinic orbits of Unified Lorenz-Type System (ULTS). Other than the known results that the ULTS has two homoclinic orbits to E 0 = (0, 0, 0) for b = −2a 1 , d = −a 1 , a 2 1 + a 2 c > 0, e < 0 and two heteroclinic orbits to E 1,2 = (± − , a1d−a2c a2e ) while no homoclinic orbit when a 1 < 0, e < 0, a 1 + d < 0, a 2 = 0, a 2 c − a 1 d > 0, b + 2a 1 ≥ 0.

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2020

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“…How about the other cases? Issue 1.3: Particularly, the authors in [5,39] rigorously proved that there exists a pair of symmetrical heteroclinic orbits in the unified Lorenz-type system and hyperchaotic Lorenz-type system by aid of Lyapunov function, concepts of both αlimit set and ω-limit set. Whether does the system (1) have this kind of dynamics in the region of parameters other than the one given in [5,Theorem 5,p.…”

mentioning

confidence: 99%

“…How about the other cases? Issue 1.3: Particularly, the authors in [5,39] rigorously proved that there exists a pair of symmetrical heteroclinic orbits in the unified Lorenz-type system and hyperchaotic Lorenz-type system by aid of Lyapunov function, concepts of both αlimit set and ω-limit set. Whether does the system (1) have this kind of dynamics in the region of parameters other than the one given in [5,Theorem 5,p.…”

mentioning

confidence: 99%

“…Existence of herteroclinic orbit. Utilizing two different Lyapunov functions, concepts of both α-limit set and ω-limit set [5,16,17,19,20,21,24,34,35,39,40,41,44,45], this section devotes to investigating the existence of heteroclinic orbits of the system (1), aiming at complementing and extending the obtained results in [5,Theorem 5,p.579]. The fundamental work of the proof is how to construct suitable Lyapunov functions for the system (1).…”

mentioning

confidence: 99%