Global Dynamics and Bifurcations Analysis of a Two-Dimensional Discrete-Time Lotka-Volterra Model

Table 1

Number of equilibria along with qualitative behavior.

EP	Corresponding behavior
	Sink if and ; source if and ; saddle if and ; nonhyperbolic if or .
	Sink if and ; never source; saddle if and ; nonhyperbolic if .
	Sink if and ; never source; saddle if and ; nonhyperbolic if .
	Locally asymptotically stable if .
	Unstable if
	Locally asymptotically stable if and only if
	Repeller if and only if
	,
	Saddle if and only if
	,
	Nonhyperbolic if and only if
	Locally asymptotically stable focus if
	Unstable focus if
	Nonhyperbolic (under which the eigenvalues are a pair of complex conjugates with modulus 1) if