Stability and Hopf bifurcation analysis in a fractional-order delayed paddy ecosystem

Stability and Hopf bifurcation analysis in a fractional-order delayed paddy ecosystem

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Abstract By introducing a delayed fractional-order differential equation model, we deal with the dynamics of the iphone 14 price texas stability and Hopf bifurcation of a paddy ecosystem with three main components: rice, weeds, and inorganic fertilizer.In the system, there exists an equilibrium for rice and weeds extinction and an equilibrium for rice extinction or weeds extinction.We obtain sufficient conditions read more for the stability and Hopf bifurcation by analyzing their characteristic equation.Some numerical simulations validate our theoretical results.