Fractional-Order Periodic Maps: Stability Analysis and Application to the Periodic-2 Limit Cycles in the Nonlinear Systems

We consider the stability of periodic map with period-2 in linear fractional difference equations where the function is f ( x ) = a x at even times and f ( x ) = b x at odd times. The stability of such a map for an integer order map depends on product ab . The conditions are much complex for fractio...

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Bibliographic Details
Published inJournal of nonlinear science Vol. 33; no. 6
Main Authors Bhalekar, Sachin, Gade, Prashant M.
Format Journal Article
LanguageEnglish
Published New York Springer US 01.12.2023
Springer Nature B.V
Subjects
Analysis
Classical Mechanics
Difference equations
Economic Theory/Quantitative Economics/Mathematical Methods
Mathematical and Computational Engineering
Mathematical and Computational Physics
Mathematics
Mathematics and Statistics
Nonlinear systems
Orbits
Stability analysis
Theoretical
39A30
Periodic map
Fractional order
Stability
37E05
26A33
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Summary:We consider the stability of periodic map with period-2 in linear fractional difference equations where the function is f ( x ) = a x at even times and f ( x ) = b x at odd times. The stability of such a map for an integer order map depends on product ab . The conditions are much complex for fractional maps and depend on ab as well as a + b . There are no superstable period-2 orbits. These conditions are useful in obtaining stability conditions of asymptotically periodic orbits with period-2 in the nonlinear case. The stability conditions are demonstrated numerically. The formalism can be generalized to higher periods.
ISSN:0938-8974
1432-1467
DOI:10.1007/s00332-023-09978-y