Asymptotically period-doubling and Neimark–Sacker bifurcation controls of discrete fractional predator–prey systems

Hu-Shuang Hou, Guo-Cheng Wu, René Lozi and Zhi-Wen Mo

Chaos, Solitons & Fractals, 2026, vol. 208, issue P1

Abstract: Fractional calculus is a new dimension to describe the complexity of nonlinear systems, but it also leads to difficulty in bifurcation control. This paper provides analytical conditions for actively controlling bifurcations in discrete fractional predator–prey systems, whereas existing studies primarily rely on numerical observations. A rigorous analytical method is established to control both Neimark–Sacker and period-doubling bifurcations. Through eigenvalue analysis, the conditions for the onset of these bifurcations are first derived. Then, it is shown how hybrid and state-feedback controllers can systematically suppress them. Numerical simulations confirm the effectiveness of the theoretical results, providing a solid analytical foundation for managing complex dynamics in ecological systems. The method can also be used in bifurcation controlling in other fractional discrete-time systems.

Keywords: Discrete fractional calculus; Predator–prey system; Bifurcation control (search for similar items in EconPapers)
Date: 2026
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Persistent link: https://EconPapers.repec.org/RePEc:eee:chsofr:v:208:y:2026:i:p1:s0960077926002195

DOI: 10.1016/j.chaos.2026.118078

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