A Novel Highly Nonlinear Quadratic System: Impulsive Stabilization, Complexity Analysis, and Circuit Designing
This work introduces a three-dimensional, highly nonlinear quadratic oscillator with no linear terms in its equations. Most of the quadratic ordinary differential equations (ODEs) such as Chen, Rossler, and Lorenz have at least one linear term in their equations. Very few quadratic systems have been...
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| Main Authors: | , , , , , |
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| Format: | Article |
| Language: | English |
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Wiley
2022-01-01
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| Series: | Complexity |
| Online Access: | http://dx.doi.org/10.1155/2022/6279373 |
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| _version_ | 1832562182703808512 |
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| author | Arthanari Ramesh Alireza Bahramian Hayder Natiq Karthikeyan Rajagopal Sajad Jafari Iqtadar Hussain |
| author_facet | Arthanari Ramesh Alireza Bahramian Hayder Natiq Karthikeyan Rajagopal Sajad Jafari Iqtadar Hussain |
| author_sort | Arthanari Ramesh |
| collection | DOAJ |
| description | This work introduces a three-dimensional, highly nonlinear quadratic oscillator with no linear terms in its equations. Most of the quadratic ordinary differential equations (ODEs) such as Chen, Rossler, and Lorenz have at least one linear term in their equations. Very few quadratic systems have been introduced and all of their terms are nonlinear. Considering this point, a new quadratic system with no linear term is introduced. This oscillator is analyzed by mathematical tools such as bifurcation and Lyapunov exponent diagrams. It is revealed that this system can generate different behaviors such as limit cycle, torus, and chaos for its different parameters’ sets. Besides, the basins of attractions for this system are investigated. As a result, it is revealed that this system’s attractor is self-excited. In addition, the analog circuit of this oscillator is designed and analyzed to assess the feasibility of the system’s chaotic solution. The PSpice simulations confirm the theoretical analysis. The oscillator’s time series complexity is also investigated using sample entropy. It is revealed that this system can generate dynamics with different sample entropies by changing parameters. Finally, impulsive control is applied to the system to represent a possible solution for stabilizing the system. |
| format | Article |
| id | doaj-art-5526ae05ce2e462fa6179fa7ec5c675e |
| institution | Kabale University |
| issn | 1099-0526 |
| language | English |
| publishDate | 2022-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Complexity |
| spelling | doaj-art-5526ae05ce2e462fa6179fa7ec5c675e2025-02-03T01:23:13ZengWileyComplexity1099-05262022-01-01202210.1155/2022/6279373A Novel Highly Nonlinear Quadratic System: Impulsive Stabilization, Complexity Analysis, and Circuit DesigningArthanari Ramesh0Alireza Bahramian1Hayder Natiq2Karthikeyan Rajagopal3Sajad Jafari4Iqtadar Hussain5Centre for Materials ResearchDepartment of Biomedical EngineeringInformation Technology CollageCentre for Nonlinear SystemsDepartment of Biomedical EngineeringMathematics ProgramThis work introduces a three-dimensional, highly nonlinear quadratic oscillator with no linear terms in its equations. Most of the quadratic ordinary differential equations (ODEs) such as Chen, Rossler, and Lorenz have at least one linear term in their equations. Very few quadratic systems have been introduced and all of their terms are nonlinear. Considering this point, a new quadratic system with no linear term is introduced. This oscillator is analyzed by mathematical tools such as bifurcation and Lyapunov exponent diagrams. It is revealed that this system can generate different behaviors such as limit cycle, torus, and chaos for its different parameters’ sets. Besides, the basins of attractions for this system are investigated. As a result, it is revealed that this system’s attractor is self-excited. In addition, the analog circuit of this oscillator is designed and analyzed to assess the feasibility of the system’s chaotic solution. The PSpice simulations confirm the theoretical analysis. The oscillator’s time series complexity is also investigated using sample entropy. It is revealed that this system can generate dynamics with different sample entropies by changing parameters. Finally, impulsive control is applied to the system to represent a possible solution for stabilizing the system.http://dx.doi.org/10.1155/2022/6279373 |
| spellingShingle | Arthanari Ramesh Alireza Bahramian Hayder Natiq Karthikeyan Rajagopal Sajad Jafari Iqtadar Hussain A Novel Highly Nonlinear Quadratic System: Impulsive Stabilization, Complexity Analysis, and Circuit Designing Complexity |
| title | A Novel Highly Nonlinear Quadratic System: Impulsive Stabilization, Complexity Analysis, and Circuit Designing |
| title_full | A Novel Highly Nonlinear Quadratic System: Impulsive Stabilization, Complexity Analysis, and Circuit Designing |
| title_fullStr | A Novel Highly Nonlinear Quadratic System: Impulsive Stabilization, Complexity Analysis, and Circuit Designing |
| title_full_unstemmed | A Novel Highly Nonlinear Quadratic System: Impulsive Stabilization, Complexity Analysis, and Circuit Designing |
| title_short | A Novel Highly Nonlinear Quadratic System: Impulsive Stabilization, Complexity Analysis, and Circuit Designing |
| title_sort | novel highly nonlinear quadratic system impulsive stabilization complexity analysis and circuit designing |
| url | http://dx.doi.org/10.1155/2022/6279373 |
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