Modification of Nicholson–Bailey model under refuge effects with stability, bifurcation, and chaos control

Abstract

In this article, a modification is proposed for the classical Nicholson–Bailey model. It is assumed that the modified model follows all axioms of Nicholson–Bailey model except that in every generation a fraction of the hosts have a safe refuge from attack of parasitoids. It is investigated that under this assumption the modified model has stable coexistence. Furthermore, Neimark–Sacker bifurcation is interrogated at positive steady-state of modified model by implementing the normal forms theory of bifurcation. Chaos control methods based on perturbation of parameter and state feedback strategy are implemented to escape the trajectories from bifurcating and chaotic behavior. Furthermore, numerical simulations are carried out for illustration of theoretical discussion. Finally, all theoretical discussion is illustrated by taking into account real observed field data of host–parasitoid interaction.

The Diffusion-Driven Instability for a General Time-Space Discrete Host-Parasitoid Model

“…Tere is a clear intergenerational relationship between both host and parasitoid, so constructing a discrete model to describe them is more in line with objective reality. Readers interested in more host-parasitoid models are referred to [28][29][30][31][32][33][34] and references therein. Considering that both host and parasitoid have self-difusion behavior in space, we will investigate and analyze a general time-space discrete host-parasitoid model in this paper.…”

Dynamic modelling and chaos control for a thin plate oscillator using Bubnov–Galerkin integral method

“…The goal is to effectively obtain the desired periodic orbit or suppress chaotic behavior through suitable strategies and methods. [31][32][33][34] Consequently, the effective suppression and control of chaos hold significant practical significance. In the proposed thin plate oscillator, chaos is controlled through the application of state feedback methods.…”

Fractional-Order sliding mode control of a 4D memristive chaotic system

“…In 1990, the OGY method was developed to realize the control of chaos (Ott et al, 1990). Later, researchers developed many methods to control chaotic behavior, such as active (Agrawal et al, 2012), passive (Kuntanapreeda and Sangpet, 2012), time-delay feedback (Ge et al, 2014), linear feedback (Sun et al, 2009), sliding-mode (Li and Liu, 2010), nonlinear control (Boubakir and Labiod, 2022; Din et al, 2021; Kizmaz et al, 2019), and linear quadratic regulator-based control (Alexander et al, 2023). Among the nonlinear control methods, sliding mode control (SMC) has superb advantages, such as being robust against disturbances, sensor noises, and ensuring well-tracking dynamics.…”