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

Table 1

Detail parameters setting for different systems.

F-O systems	Unknown	Lower boundary	Upper boundary	Step	NOSP^a
Example 1	(𝜎, 𝛾, 𝑏, 𝑞1, 𝑞2, 𝑞3)	5, 20, 0.1, 0.1, 0.1, 0.1	15, 30, 10, 1, 1, 1	0.01	100
Example 2	(𝛽1, 𝛽2, 𝛽3, 𝛽4, 𝑞1, 𝑞2, 𝑞3)	−6, 2, 0.1, −1.5, 0.1, 0.1, 0.1	−5, 5, 1, −0.5, 1, 1, 1	0.005	200
Example 3	(𝑎, 𝑏, 𝑐, 𝑞1, 𝑞2)	0.1, 0.1, 0.1, 0.1, 0.5	1, 1, 2, 1, 1.5	0.0005	500
Example 4	(𝛽1, 𝛽2, 𝛽3, 𝛽4, 𝑞1, 𝑞2, 𝑞3)	1, 1, 0.1, 0.1, 0.5, 0.5, 0.1	2, 2, 1, 1.5, 1.5, 1.5, 1	0.005	200
Example 5	(𝑎, 𝑏, 𝑐, 𝑞1, 𝑞2, 𝑞3)	0.5, 0.01, 0.5, 0.5, 0.1, 0.1	1.5, 1, 1.5, 1.5, 1, 1	0.005	200
Example 6	(𝑎, 𝑏, 𝑐, 𝑞1, 𝑞2, 𝑞3)	30, 0.1, 15, 0.1, 0.1, 0.1	40, 10, 25, 1, 1, 1	0.01	100
Example 7	(𝑎, 𝑏, 𝑐, 𝑑, 𝑞1, 𝑞2, 𝑞3)	30, 0.1, 20, −10, 0.5, 1, 1	40, 10, 30, −0.1, 2, 2, 2	0.01	100
Example 8	(𝑎, 𝑏, 𝑐, 𝑞1, 𝑞2, 𝑞3)	0.1, 0.1, 5, 0.1, 0.1, 0.1	1, 1, 15, 1, 1, 1	0.01	100
Example 9	(𝛼, 𝛽, 𝛾, 𝜁, 𝑎, 𝑏, 𝑞1, 𝑞2, 𝑞3, 𝑞4)	5, 10, 0.1, 0.1, 0.3, 0.1, 0.1, 0.1, 0.1, 0.1	10, 20, 1, 2, 0.3, 1, 1, 1, 1, 1	0.01	100
Example 10	(𝑎, 𝑏, 𝑐, 𝑑, 𝑞1, 𝑞2, 𝑞3, 𝑞4)	5, 0.1, 20, −2, 0.1, 0.1, 0.1, 0.1	15, 5, 30, −0.1, 1, 1, 1, 1	0.01	100
Example 11	(𝑎, 𝑏, 𝑐, 𝑑, 𝑞1, 𝑞2, 𝑞3, 𝑞4)	30, 0.1, 15, 0.1, 0.1, 0.1, 0.1, 0.1	40, 5, 25, 5, 1, 1, 1, 1	0.005	200
Example 12	(𝑎, 𝑏, 𝑐, 𝑑, 𝑞1, 𝑞2, 𝑞3, 𝑞4)	5, 0.5, 1, 0.1, 0.1, 0.1, 0.1, 0.1	15, 1.5, 10, 1, 1, 1, 1, 1	0.005	100
Example 13	(𝑎, 𝑏, 𝑐, 𝑑, 𝑞1, 𝑞2, 𝑞3, 𝑞4)	30, 0.1, 10, 0.1, 0.1, 0.1, 0.1, 0.1, 0.1	40, 5, 20, 10, 1, 1, 1, 1, 1	0.005	200
Example 14	(𝑎, 𝑏, 𝑐, 𝑑, 𝑞1, 𝑞2, 𝑞3, 𝑞4)	0.1, 0.1, 0.1, 0.01, 0.1, 0.1, 0.1, 0.1	1, 5, 1, 1, 1, 1, 1, 1	0.005	200
Example 15	(𝑎, 𝑏, 𝑐, 𝑞1, 𝑞2, 𝑞3, 𝑞4)	5, 38, 45, 0.5, 0.5, 0.5, 0.5	10, 45, 50, 1, 1, 1, 1	0.005	200

aNumber of sample points for resolving the fractional chaos systems.