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. 2023 Nov 30;33(2):689–746. doi: 10.1007/s12591-023-00666-7

Table 2.

The local phase portraits at the finite and infinite equilibrium points of the continuous piecewise differential systems (I)

Systems Conditions Finite equilibrium points Infinite equilibrium points
(I) (I-1): σ<-2 P+(stable node) p+(saddle)
p-(unstable node)
P-(saddle) q+(stable node)
q-(unstable node)
(I-2): σ=-2 P+(stable node) p(semi-hyperbolic saddle-node)
P-(saddle) q+(stable node)
q-(unstable node)
(I-3): -2<σ<0 P+(stable focus)
P-(saddle) q+(stable node)
q-(unstable node)
(I-4): σ=0 P+(center)
P-(saddle) q+(stable node)
q-(unstable node)
(I-5): 0<σ<2 P+(unstable focus)
P-(saddle) q+(stable node)
q-(unstable node)
(I-6): σ=2 P+(unstable node) p(semi-hyperbolic saddle-node)
P-(saddle) q+(stable node)
q-(unstable node)
(I-7): σ>2 P+(unstable node) p+(stable node)
p-(saddle)
P-(saddle) q+(stable node)
q-(unstable node)