Stable and Unstable Periodic Solutions of Reduced Dynamic Systems with Local Nonlinearities

1990 ◽  
pp. 247-254
Author(s):  
R. H. B. Fey ◽  
A. de Kraker ◽  
D. H. van Campen ◽  
G. J. Meijer
Keyword(s):  
Periodic Solutions ◽  
Dynamic Systems ◽  
Reduced Dynamic

Further Remarks on the Existence of Periodic Solutions of Linear Time Varying Periodic Fractional Order Systems

2017 ◽  
Author(s):  
XueFeng Zhang ◽  
YangQuan Chen
Keyword(s):  
Laplace Transform ◽  
Periodic Solutions ◽  
Fractional Order ◽  
Dynamic Systems ◽  
Linear Time ◽  
Periodic Systems ◽  
Time Varying ◽  
Fractional Order Systems ◽  
Order Linear ◽  
Existence Of Periodic Solutions

Existence of periodic solutions of fractional order dynamic systems is an important and difficult issue in fractional order systems field. In this paper, the non existence of completely periodic solutions and existence of partly periodic solutions of fractional order linear time varying periodic systems and fractional order nonlinear time varying periodic systems are discussed. A new property of Laplace transform of periodic function is derived. The non existences of completely periodic solutions of fractional order linear time varying periodic systems and fractional order nonlinear time varying periodic fractional order systems are presented by Laplace transform method and contradiction approach. The existence of partly periodic solutions of fractional order dynamic systems are proved by constructing numerical examples and considering Laplace transform property approaches. The examples and state figures are given to illustrate the effectiveness of conclusion presented.

scholarly journals Nonnegative Periodic Solutions of a Three-Term Recurrence Relation Depending on Two Real Parameters

2017 ◽  
Vol 2017 ◽  
pp. 1-21 ◽  
Author(s):  
Yen Chih Chang ◽  
Sui Sun Cheng ◽  
Wei Chang Yeh
Keyword(s):  
Periodic Solutions ◽  
Dynamic Systems ◽  
Recurrence Relations ◽  
Geometric Approach ◽  
Time Varying ◽  
Special Interests ◽  
Variation Of Parameters ◽  
Simulation Results ◽  
Bang Bang Control ◽  
Three Term Recurrence Relation

Simple dynamic systems representing time varying states of interconnected neurons may exhibit extremely complex behaviors when bifurcation parameters are switched from one set of values to another. In this paper, motivated by simulation results, we examine the steady states of one such system with bang-bang control and two real parameters. We found that nonnegative and negative periodic states are of special interests since these states are solutions of linear nonhomogeneous three-term recurrence relations. Although the standard approach to analyse such recurrence relations is the method of finding the general solutions by means of variation of parameters, we find novel alternate geometric methods that offer the tracking of solution trajectories in the plane. By means of this geometric approach, we are then able, without much tedious computation, to completely characterize the nonnegative and negative periodic solutions in terms of the bifurcation parameters.

scholarly journals Periodic solutions of almost linear Volterra integro-dynamic systems

2020 ◽  
Vol 8 (4) ◽  
pp. 1427-1433
Author(s):  
Abderrahim Guerfi ◽  
Abdelouaheb Ardjouni
Keyword(s):  
Periodic Solutions ◽  
Dynamic Systems
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