Vallis system is a model describing nonlinear interactions of the atmosphere and temperature fluctuations with a strong influence in the equatorial part of the Pacific Ocean. As the model approaches the fractional order from the integer order, numerical simulations for different situations arise. To see the behavior of the simulations, several cases involving integer analysis with different non-integer values of the Vallis systems were applied. In this work, a fractional mathematical model is constructed using the Caputo derivative. The local asymptotic stability of the equilibrium points of the fractional-order model is obtained from the fundamental production number. The chaotic behavior of this system is studied using the Caputo derivative and Lyapunov stability theory. Hopf bifurcation is used to vary the oscillation of the system in steady and unsteady states. In order to perform these numerical simulations, we apply Grunwald-Letnikov tactics with Binomial coefficients to obtain the effects on the non-integer fractional degree and discrete time vallis system and plot the phase diagrams and phase portraits with the help of MATLAB and MAPLE packages.

山谷系统是描述大气与温度波动的非线性相互作用的模型，对太平洋赤道部分影响很大。当模型从整数阶接近分数阶时，会出现不同情况的数值模拟。为了观察模拟的行为，应用了涉及对 Vallis 系统的不同非整数值进行整数分析的几种情况。在这项工作中，使用 Caputo 导数构建了分数阶数学模型。分数阶模型平衡点的局部渐近稳定性是从基本产生数获得的。利用 Caputo 导数和 Lyapunov 稳定性理论研究了该系统的混沌行为。Hopf 分岔用于改变系统在稳态和非稳态下的振荡。为了执行这些数值模拟，我们应用具有二项式系数的 Grunwald-Letnikov 策略来获得对非整数分数阶和离散时间山谷系统的影响，并借助 MATLAB 和 MAPLE 软件包绘制相图和相图。