Parameters Estimation and Stability Analysis of Nonlinear Fractional-Order Economic System Based on Empirical Data

Table 1

Optimal parameters of fractional order economic system for US, Australia, UK.

	US				Australia				UK
	𝑥	𝑦	𝑧		𝑥	𝑦	𝑧		𝑥	𝑦	𝑧
𝑞	0.298	0.518	1.521		0.459	0.127	1.992		0.503	0.521	0.611
𝑐̂	0.141	0.845	−42.503		0.936	0.128	0.957		1.271	1.618	0.959
𝑎.1	−7.360	−26.756	19.654		9.923	−2.817	3.007		−10.655	−70.531	−13.637
𝑎.2	10.596	42.678	−45.415		2.352	2.855	2.661		−85.040	54.652	19.055
𝑎.3	−208.649	−82.896	−3.255		1.696	−4.907	−1.889		−91.272	−73.995	100.756
𝑎.4	106.886	134.066	7.465		1.011	2.837	−1.094		37.836	98.484	−31.076
𝑎.5	−92.283	−29.489	−9.162		6.746	−13.460	−0.854		−28.490	−60.796	17.146
𝑎.6	−46.156	0.388	−9.954		−10.966	−8.466	−6.662		0.939	37.492	2.462
𝑎.7	−40.568	24.615	33.139		1.639	−9.793	−1.183		−31.064	−46.859	2.666
𝑎.8	−28.753	98.083	−19.133		0.152	14.682	2.982		65.905	28.800	32.485
𝑎.9	−17.425	−18.006	−19.731		−4.210	0.094	−1.558		−18.148	−34.796	3.771
MSE	4.8𝑒−4				6.6𝑒−4				5.5𝑒−4

Notes: 𝑐̂ denote the (𝑐₁̂,𝑐₂̂,𝑐₃̂). 𝑎_.𝑖 denote (𝑎_1𝑖,𝑎_2𝑖,𝑎_3𝑖)  (𝑖=1,2,…,9). MSE is mean of squared error.