Page 543 - Mathematical Techniques of Fractional Order Systems

522 Mathematical Techniques of Fractional Order Systems

TABLE 17.5 System (2) Responses Versus the Fractional Order α at
Parameter Value a 5 0:4
α 5 0:96 α 5 0:98 α 5 1
Divergent Periodic Chaotic

TABLE 17.6 System (16) Responses Versus the Fractional Order α at
Parameter Value a 5 1
α 5 0:79 α 5 0:95 α 5 0:98 α 5 1
Divergent Periodic Quasi-Periodic Chaotic

with the initial point marked in red, illustrating the obtained type of solution
(periodic or chaotic) for different values of the fractional order.
Sensitivities of some other systems to parameter variations and fractional
orders were tested. For example, system (4) is characterized by high sensitiv-
ity to parameter variation, where it diverges for values of a slightly lower or
higher than 1:0. It is similarly sensitive to variations in the fractional order α
and diverges for values slightly lower than 1:0.