Identification of Unknown Parameters and Orders via Cuckoo Search Oriented Statistically by Differential Evolution for Noncommensurate Fractional-Order Chaotic Systems

Table 2

Simulation results for different fractional-order chaos systems by CSODE.

F-O system	StD	Mean	Min.	Max.	Success rate^a	NEOF^b
Example 1	2.2025𝑒−04	6.6862𝑒−04	3.1179𝑒−06	5.5594𝑒−03	100%	24013
Example 2	4.7346𝑒−06	1.5061𝑒−05	3.2217𝑒−07	1.4355𝑒−04	100%	24073
Example 3	5.8073𝑒−09	1.4890𝑒−08	1.3035𝑒−10	1.3548𝑒−07	100%	24016
Example 4	1.3724𝑒−04	5.1929𝑒−04	7.6119𝑒−07	3.8262𝑒−03	100%	24073
Example 5	2.7967𝑒−08	2.9039𝑒−08	1.5084𝑒−09	1.4728𝑒−07	100%	24013
Example 6	2.7950𝑒−04	6.5471𝑒−04	6.8653𝑒−06	5.9367𝑒−03	100%	24038
Example 7	6.5650𝑒−03	8.3188𝑒−03	1.6981𝑒−04	4.3289𝑒−02	83%	24074
Example 8	1.8666𝑒−08	2.1368𝑒−08	1.2494𝑒−09	1.2324𝑒−07	100%	24013
Example 9	1.4857𝑒−04	1.4529𝑒−04	1.9011𝑒−05	1.0265𝑒−03	100%	24073
Example 10	5.1741𝑒−03	4.4624𝑒−03	5.0835𝑒−04	2.4994𝑒−02	87%	24041
Example 11	1.2904𝑒−02	1.2573𝑒−02	5.8260𝑒−04	5.5329𝑒−02	100%^c	24041
Example 12	6.2490𝑒−06	4.1206𝑒−06	3.3623𝑒−07	2.3320𝑒−05	100%	24101
Example 13	5.4440𝑒−02	4.5710𝑒−02	6.0972𝑒−03	2.7476𝑒−01	87%^c	24022
Example 14	2.0859𝑒−04	1.5394𝑒−04	3.1938𝑒−05	7.9808𝑒−04	100%	24041
Example 15	4.5612𝑒−01	1.8007𝑒+00	3.1952𝑒−03	1.6640𝑒+01	56%^c	24024

aSuccess means that the solution is less than 1𝑒−2 in 100 independent simulations.
bNo. of average evaluation for objective function (NEOF).
cSuccess means that the solution is less than 1𝑒−1 in 100 independent simulations.