Neimark‐Sacker bifurcation and hybrid control in a discrete‐time Lotka‐Volterra model.

We explore the local dynamics, N‐S bifurcation, and hybrid control in a discrete‐time Lotka‐Volterra predator‐prey model in R+2. It is shown that ∀ parametric values, model has two boundary equilibria: P00(0,0) and Px0(1,0), and a unique positive equilibrium point: Pxy+dc,rc−dbc if c>d. We explored the local dynamics along with different topological classifications about equilibria: P00(0,0), Px0(1,0), and Pxy+dc,rc−dbc of the model. It is proved that model cannot undergo any bifurcation about P00(0,0) and Px0(1,0) but it undergoes an N‐S bifurcation when parameters vary in a small neighborhood of Pxy+dc,rc−dbc by using a center manifold theorem and bifurcation theory and meanwhile, invariant close curves appears. The appearance of these curves implies that there exist a periodic or quasiperiodic oscillations between predator and prey populations. Further, theoretical results are verified numerically. Finally, the hybrid control strategy is applied to control N‐S bifurcation in the discrete‐time model. [ABSTRACT FROM AUTHOR]