There exist six equilibrium points , , , , , and , where and are locally asymptotically stable, , , and are saddle points, and is repeller. The stable manifold of the saddle point is an increasing separatrix with endpoint at , and solutions with initial point above the converge to , while solutions with initial point below the converge to All orbits that start on are attracted to The basins of attraction of and are, respectively, and
(ii)
, , ,
There exist five equilibrium points , , , , and , where is locally asymptotically stable, and are saddle points, is repeller, and is nonhyperbolic. There exists a continuous increasing curve with endpoint at , which is a subset of the basin of attraction of . All solutions with initial point above converge to , while solutions with initial point below converge to The basins of attraction of and are, respectively, and
(iii)
, ,
There exist five equilibrium points , , , , and , where and are locally asymptotically stable, and are saddle points, and is repeller. The stable manifold of the saddle point is an increasing separatrix with endpoint at , and solutions with initial point above converge to , while solutions with initial point below converge to . All orbits that start on are attracted to . The basin of attraction of is
(iv)
, , or , , ,
There exist four equilibrium points , , , and , where is globally asymptotically stable, and are saddle points, and is a repeller. The basins of attraction of , , and are, respectively, , , and
(v)
, , ,
There exist four equilibrium points , , , and , where and are locally asymptotically stable and and are saddle points. The stable manifold of the saddle point is an increasing separatrix, and solutions with initial point above converge to , while solutions with initial point below converge to All orbits that start on are attracted to The basin of attraction of is given by
(vi)
, , ,
There exist five equilibrium points , , , , and , where is locally asymptotically stable, and are saddle points, is nonhyperbolic, and is a repeller. The stable manifold of the saddle point is an increasing separatrix with endpoint at , and solutions with initial point above converge to , while solutions with initial point below converge to All orbits that start on are attracted to The basin of attraction of is given by
(vii)
, , ,
There exist four equilibrium points , , , and , where is locally asymptotically stable, is a saddle point, is nonhyperbolic, and is a repeller. There exists a strictly increasing curve with endpoint at , which is the subset of the basin of attraction of . All solutions with initial point above converge to , while solutions with initial point below converge to The basin of attraction of is given by
(viii)
, , ,
There exist five equilibrium points , , , and , where is locally asymptotically stable, is a saddle point, is nonhyperbolic, and is a repeller. The basins of attraction of and are given by and and the basin of attraction of is
(ix)
, , ,
There exist four equilibrium points , , , and , where and are locally asymptotically stable, is a saddle point, and is nonhyperbolic. There exist continuous increasing curves and with endpoint at , which are the subsets of the basin of attraction of . Further, all solutions with initial point above converge to and all solutions with initial point above and below converge to , while solutions with initial point below converge to The basin of attraction of is
(x)
, ,
There exist three equilibrium points , , and , where is locally asymptotically stable, is a saddle point, and is nonhyperbolic. There exists a continuous increasing curve with endpoint at which is a subset of the basin of attraction of . All solutions with initial point above converge to , while solutions with initial point below converge to The basin of attraction of is given by
(xi)
,
There exist two equilibrium points , which is a saddle point, and , which is globally asymptotically stable, where and
(xii)
,
There exist three equilibrium points , , and , where is nonhyperbolic, is locally asymptotically stable, and is a saddle point. The stable manifold of the saddle point is an increasing separatrix with endpoint at , and solutions with initial point above converge to , while solutions with initial point below converge to All orbits that start on are attracted to The basin of attraction of is given by
(xiii)
,
There exist two equilibrium points and which are nonhyperbolic. There exists a continuous increasing curve with endpoint at which is a subset of the basin of attraction of . All solutions with initial point above converge to , while solutions with initial point below converge to
(xiv)
,
There exists one equilibrium point which is nonhyperbolic and global attractor. The basin of attraction of is
(xv)
,
There exist three equilibrium points , , and , where and are locally asymptotically stable and is a saddle point. The stable manifold of the saddle point is an increasing separatrix with endpoint at , and solutions with initial point above converge to , while solutions with initial point below converge to All orbits that start on are attracted to
(xvi)
,
There exists one equilibrium point which is globally asymptotically stable. The basin of attraction of is
(xvii)
,
There exist two equilibrium points and , where is locally asymptotically stable and is nonhyperbolic. There exists a continuous increasing curve with endpoint at which is a subset of the basin of attraction of . All solutions with initial point above converge to , while solutions with initial point below converge to
