论文标题
涉及立方非线性的分数延迟差分方程的稳定性和分叉分析
Stability and Bifurcation Analysis of a Fractional Order Delay Differential Equation Involving Cubic Nonlinearity
论文作者
论文摘要
分数衍生物和延迟是对自然系统中的内存属性进行建模的重要工具。这项工作涉及分数阶延迟差分方程的稳定性分析\ begin {qore*} d^αx（t）=ΔX（t-τ）-εx（t-τ）（t-τ）^3-px（t）^2+q x（t）。 \ end {方程*}我们在平衡点附近提供该系统的线性化，并提出线性化稳定性条件。为了讨论平衡点的稳定性，我们建议有关参数$δ$，$ε$，$ p $，$ q $和$τ$的各种条件。即使系统中涉及五个参数，我们也能够以任何正$ε$和$ p $提供$qδ-$平面的稳定区域草图。这提供了系统稳定性的完整分析。此外，我们研究了提出的模型中的混乱。该系统表现出有关广泛延迟参数的混乱。
Fractional derivative and delay are important tools in modeling memory properties in the natural system. This work deals with the stability analysis of a fractional order delay differential equation \begin{equation*} D^αx(t)=δx(t-τ)-εx(t-τ)^3-px(t)^2+q x(t). \end{equation*} We provide linearization of this system in a neighbourhood of equilibrium points and propose linearized stability conditions. To discuss the stability of equilibrium points, we propose various conditions on the parameters $δ$, $ε$, $p$, $q$ and $τ$. Even though there are five parameters involved in the system, we are able to provide the stable region sketch in the $qδ-$plane for any positive $ε$ and $p$. This provides the complete analysis of stability of the system. Further, we investigate chaos in the proposed model. This system exhibits chaos for a wide range of delay parameter.
