Bifurcation of Limit Cycles by Perturbing a Piecewise Linear Hamiltonian System

Table 1

Coefficient conditions for phase portraits (1)–(13).

Coefficient; conditions	𝑎1≥0,𝑎0≥0	𝑎1>0	𝑎1≤0,𝑎0≤0	𝑎1<0
	𝑎1+𝑎0>0	𝑎0<0	𝑎1+𝑎0<0	𝑎0>0
𝑏1≥0,𝑏0≤0,𝑏1>𝑏0	(1)	(2)		(5)
𝑏1>0,𝑏0>0	(3)	(4)	(7)	(9)
𝑏1≤0,𝑏0≥0,𝑏0>𝑏1		(8)
				(11) (𝑎^20𝑏1=𝑎1𝑏^20),
𝑏1<0,𝑏0<0	(6)	(10)		(12) (𝑎^20𝑏1>𝑎1𝑏^20),
				(13) (𝑎^20𝑏1<𝑎1𝑏^20)