Chaos Prediction in Fractional Delayed Energy-Based Models of Capital Accumulation
This paper presents the nonlinear dynamic analysis of energy-based models arisen from the applied systems characterized by the energy transport in the presence of fractional order derivative and time delay. The studied model is the fractional version of Bianca-Ferrara-Dalgaard-Strulik (BFDS) model o...
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| Format: | Article |
| Language: | English |
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Wiley
2021-01-01
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| Series: | Complexity |
| Online Access: | http://dx.doi.org/10.1155/2021/8751963 |
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| author | Mohamed El-Borhamy Tamer Medhat Manal E. Ali |
| author_facet | Mohamed El-Borhamy Tamer Medhat Manal E. Ali |
| author_sort | Mohamed El-Borhamy |
| collection | DOAJ |
| description | This paper presents the nonlinear dynamic analysis of energy-based models arisen from the applied systems characterized by the energy transport in the presence of fractional order derivative and time delay. The studied model is the fractional version of Bianca-Ferrara-Dalgaard-Strulik (BFDS) model of economy which is viewed as a transport network for energy in which the law of motion of capital occurs. By considering the time delay as bifurcation parameter, a proof to investigate the existence of Hopf bifurcation and the phase lock solutions using the Poincare-Linstedt and the harmonic balance methods is given. At definite values of time delay, period-doubling bifurcations followed up by the consequences of chaotic states are detected. Simulation results assure that the BFDS model can generate new (hyper) chaotic attractors beyond half order derivatives through the effect of the time delay on that system. In accordance with the literatures related to the problem of chaos, the concluded results confirm the proposed theorem by El-Borhamy in which the time delay possesses the ability to change the dynamic state of nonlinear systems from regular to chaotic within the fractional order derivative domain. |
| format | Article |
| id | doaj-art-9649f58eff424b76bfb2071255cf6b69 |
| institution | Kabale University |
| issn | 1076-2787 1099-0526 |
| language | English |
| publishDate | 2021-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Complexity |
| spelling | doaj-art-9649f58eff424b76bfb2071255cf6b692025-02-03T05:49:51ZengWileyComplexity1076-27871099-05262021-01-01202110.1155/2021/87519638751963Chaos Prediction in Fractional Delayed Energy-Based Models of Capital AccumulationMohamed El-Borhamy0Tamer Medhat1Manal E. Ali2Department of Engineering Mathematics and Physics, Faculty of Engineering, University of Tanta, Tanta, EgyptDepartment of Electrical Engineering, Faculty of Engineering, University of Kafrelsheikh, Kafrelsheikh, EgyptDepartment of Engineering Mathematics and Physics, Faculty of Engineering, University of Kafrelsheikh, Kafrelsheikh, EgyptThis paper presents the nonlinear dynamic analysis of energy-based models arisen from the applied systems characterized by the energy transport in the presence of fractional order derivative and time delay. The studied model is the fractional version of Bianca-Ferrara-Dalgaard-Strulik (BFDS) model of economy which is viewed as a transport network for energy in which the law of motion of capital occurs. By considering the time delay as bifurcation parameter, a proof to investigate the existence of Hopf bifurcation and the phase lock solutions using the Poincare-Linstedt and the harmonic balance methods is given. At definite values of time delay, period-doubling bifurcations followed up by the consequences of chaotic states are detected. Simulation results assure that the BFDS model can generate new (hyper) chaotic attractors beyond half order derivatives through the effect of the time delay on that system. In accordance with the literatures related to the problem of chaos, the concluded results confirm the proposed theorem by El-Borhamy in which the time delay possesses the ability to change the dynamic state of nonlinear systems from regular to chaotic within the fractional order derivative domain.http://dx.doi.org/10.1155/2021/8751963 |
| spellingShingle | Mohamed El-Borhamy Tamer Medhat Manal E. Ali Chaos Prediction in Fractional Delayed Energy-Based Models of Capital Accumulation Complexity |
| title | Chaos Prediction in Fractional Delayed Energy-Based Models of Capital Accumulation |
| title_full | Chaos Prediction in Fractional Delayed Energy-Based Models of Capital Accumulation |
| title_fullStr | Chaos Prediction in Fractional Delayed Energy-Based Models of Capital Accumulation |
| title_full_unstemmed | Chaos Prediction in Fractional Delayed Energy-Based Models of Capital Accumulation |
| title_short | Chaos Prediction in Fractional Delayed Energy-Based Models of Capital Accumulation |
| title_sort | chaos prediction in fractional delayed energy based models of capital accumulation |
| url | http://dx.doi.org/10.1155/2021/8751963 |
| work_keys_str_mv | AT mohamedelborhamy chaospredictioninfractionaldelayedenergybasedmodelsofcapitalaccumulation AT tamermedhat chaospredictioninfractionaldelayedenergybasedmodelsofcapitalaccumulation AT manaleali chaospredictioninfractionaldelayedenergybasedmodelsofcapitalaccumulation |