Positive Periodic Solutions of a Periodic Discrete Competitive System Subject to Feedback Controls

Figure 4

Two-dimensional phase portrait. (a) Phase portrait of 𝑦^∗₁(𝑘) and 𝑦^∗₂(𝑘) with initial values 𝑦^∗₁(0)=1.1560 and 𝑦^∗₂(0)=1.0720 and 𝑦₁(𝑘) and 𝑦₂(𝑘) with initial values 𝑦₁(0)=1.1300 and 𝑦₂(0)=1.0850 for 𝑘∈[0,100], respectively. (b) Phase portrait of 𝑣^∗₁(𝑘) and 𝑣^∗₂(𝑘) with initial values 𝑣^∗₁(0)=0.0128 and 𝑣^∗₂(0)=0.0078 and 𝑣₁(𝑘) and 𝑣₂(𝑘) with initial values 𝑣₁(0)=0.0123 and 𝑣₂(0)=0.0071 for 𝑘∈[0,100], respectively.

(a)

(b)