Chaotic and Hyperchaotic Dynamics of a Clapp Oscillator
This paper describes recent findings achieved during a numerical investigation of the circuit known as the Clapp oscillator. By considering the generalized bipolar transistor as an active element and after applying the search-for-chaos optimization approach, parameter regions that lead to either cha...
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| Format: | Article |
| Language: | English |
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MDPI AG
2022-05-01
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| Series: | Mathematics |
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| Online Access: | https://www.mdpi.com/2227-7390/10/11/1868 |
| _version_ | 1797492612939120640 |
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| author | Jiri Petrzela |
| author_facet | Jiri Petrzela |
| author_sort | Jiri Petrzela |
| collection | DOAJ |
| description | This paper describes recent findings achieved during a numerical investigation of the circuit known as the Clapp oscillator. By considering the generalized bipolar transistor as an active element and after applying the search-for-chaos optimization approach, parameter regions that lead to either chaotic or hyperchaotic dynamics were discovered. For starters, the two-port that represents the transistor was firstly assumed to have a polynomial-forward trans-conductance; then the shape of trans-conductance changes into the piecewise-linear characteristics. Both cases cause vector field symmetry and allow the coexistence of several different attractors. Chaotic and hyperchaotic behavior were deeply analyzed by using standard numerical tools such as Lyapunov exponents, basins of attraction, bifurcation diagrams, and solution sensitivity. The structural stability of strange attractors observed numerically was finally proved via a real practical experiment: a flow-equivalent chaotic oscillator was constructed as the lumped electronic circuit, and desired attractors were captured and provided as oscilloscope screenshots. |
| first_indexed | 2024-03-10T01:06:13Z |
| format | Article |
| id | doaj.art-283a85f215b343e0ab1ad176b15e13fb |
| institution | Directory Open Access Journal |
| issn | 2227-7390 |
| language | English |
| last_indexed | 2024-03-10T01:06:13Z |
| publishDate | 2022-05-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Mathematics |
| spelling | doaj.art-283a85f215b343e0ab1ad176b15e13fb2023-11-23T14:25:57ZengMDPI AGMathematics2227-73902022-05-011011186810.3390/math10111868Chaotic and Hyperchaotic Dynamics of a Clapp OscillatorJiri Petrzela0Department of Radio Electronics, Faculty of Electrical Engineering and Communication, Brno University of Technology, Technicka 12, 616 00 Brno, Czech RepublicThis paper describes recent findings achieved during a numerical investigation of the circuit known as the Clapp oscillator. By considering the generalized bipolar transistor as an active element and after applying the search-for-chaos optimization approach, parameter regions that lead to either chaotic or hyperchaotic dynamics were discovered. For starters, the two-port that represents the transistor was firstly assumed to have a polynomial-forward trans-conductance; then the shape of trans-conductance changes into the piecewise-linear characteristics. Both cases cause vector field symmetry and allow the coexistence of several different attractors. Chaotic and hyperchaotic behavior were deeply analyzed by using standard numerical tools such as Lyapunov exponents, basins of attraction, bifurcation diagrams, and solution sensitivity. The structural stability of strange attractors observed numerically was finally proved via a real practical experiment: a flow-equivalent chaotic oscillator was constructed as the lumped electronic circuit, and desired attractors were captured and provided as oscilloscope screenshots.https://www.mdpi.com/2227-7390/10/11/1868Clapp oscillatorchaoshyperchaosLyapunov exponentsstrange attractors |
| spellingShingle | Jiri Petrzela Chaotic and Hyperchaotic Dynamics of a Clapp Oscillator Mathematics Clapp oscillator chaos hyperchaos Lyapunov exponents strange attractors |
| title | Chaotic and Hyperchaotic Dynamics of a Clapp Oscillator |
| title_full | Chaotic and Hyperchaotic Dynamics of a Clapp Oscillator |
| title_fullStr | Chaotic and Hyperchaotic Dynamics of a Clapp Oscillator |
| title_full_unstemmed | Chaotic and Hyperchaotic Dynamics of a Clapp Oscillator |
| title_short | Chaotic and Hyperchaotic Dynamics of a Clapp Oscillator |
| title_sort | chaotic and hyperchaotic dynamics of a clapp oscillator |
| topic | Clapp oscillator chaos hyperchaos Lyapunov exponents strange attractors |
| url | https://www.mdpi.com/2227-7390/10/11/1868 |
| work_keys_str_mv | AT jiripetrzela chaoticandhyperchaoticdynamicsofaclapposcillator |