A structural approach to control of transitional waves of nonlinear diffusion-reaction systems: Theory and possible applications to bio-medicine
This paper has considered a novel approach to structural recognition and control of nonlinear reaction-diffusion systems (systems with density dependent diffusion). The main consistence of the approach is interactive variation of the nonlinear diffusion and sources structural parameters that allows...
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| Format: | Article |
| Language: | English |
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Wiley
2002-01-01
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| Series: | Discrete Dynamics in Nature and Society |
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| Online Access: | http://dx.doi.org/10.1080/10260220290013499 |
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| _version_ | 1849405321344188416 |
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| author | Victor Kardashov Shmuel Einav |
| author_facet | Victor Kardashov Shmuel Einav |
| author_sort | Victor Kardashov |
| collection | DOAJ |
| description | This paper has considered a novel approach to structural recognition and control of nonlinear reaction-diffusion systems (systems with density dependent diffusion). The main consistence of the approach is interactive variation of the nonlinear diffusion and sources structural parameters that allows to implement a qualitative control and recognition of transitional system conditions (transients). The method of inverse solutions construction allows formulating the new analytic conditions of compactness and periodicity of the transients that is also available for nonintegrated systems. On the other hand, using of energy conservations laws, allows transfer to nonlinear dynamics models that gives the possiblity to apply the modern deterministic chaos theory (particularly the Feigenboum's universal constants and scenario of chaotic transitions). |
| format | Article |
| id | doaj-art-5357816309fc471385c7e65732dc259a |
| institution | Kabale University |
| issn | 1026-0226 1607-887X |
| language | English |
| publishDate | 2002-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Discrete Dynamics in Nature and Society |
| spelling | doaj-art-5357816309fc471385c7e65732dc259a2025-08-20T03:36:42ZengWileyDiscrete Dynamics in Nature and Society1026-02261607-887X2002-01-0171274010.1080/10260220290013499A structural approach to control of transitional waves of nonlinear diffusion-reaction systems: Theory and possible applications to bio-medicineVictor Kardashov0Shmuel Einav1Department of Biomedical Engineering, Tel-Aviv University, Ramat-Aviv, Tel-Aviv 69978, IsraelDepartment of Biomedical Engineering, Tel-Aviv University, Ramat-Aviv, Tel-Aviv 69978, IsraelThis paper has considered a novel approach to structural recognition and control of nonlinear reaction-diffusion systems (systems with density dependent diffusion). The main consistence of the approach is interactive variation of the nonlinear diffusion and sources structural parameters that allows to implement a qualitative control and recognition of transitional system conditions (transients). The method of inverse solutions construction allows formulating the new analytic conditions of compactness and periodicity of the transients that is also available for nonintegrated systems. On the other hand, using of energy conservations laws, allows transfer to nonlinear dynamics models that gives the possiblity to apply the modern deterministic chaos theory (particularly the Feigenboum's universal constants and scenario of chaotic transitions).http://dx.doi.org/10.1080/10260220290013499Density dependent diffusion; Structural interaction; Finite localized transients; Pulse propagations chaos degree. |
| spellingShingle | Victor Kardashov Shmuel Einav A structural approach to control of transitional waves of nonlinear diffusion-reaction systems: Theory and possible applications to bio-medicine Discrete Dynamics in Nature and Society Density dependent diffusion; Structural interaction; Finite localized transients; Pulse propagations chaos degree. |
| title | A structural approach to control of transitional waves of nonlinear diffusion-reaction systems: Theory and possible applications to bio-medicine |
| title_full | A structural approach to control of transitional waves of nonlinear diffusion-reaction systems: Theory and possible applications to bio-medicine |
| title_fullStr | A structural approach to control of transitional waves of nonlinear diffusion-reaction systems: Theory and possible applications to bio-medicine |
| title_full_unstemmed | A structural approach to control of transitional waves of nonlinear diffusion-reaction systems: Theory and possible applications to bio-medicine |
| title_short | A structural approach to control of transitional waves of nonlinear diffusion-reaction systems: Theory and possible applications to bio-medicine |
| title_sort | structural approach to control of transitional waves of nonlinear diffusion reaction systems theory and possible applications to bio medicine |
| topic | Density dependent diffusion; Structural interaction; Finite localized transients; Pulse propagations chaos degree. |
| url | http://dx.doi.org/10.1080/10260220290013499 |
| work_keys_str_mv | AT victorkardashov astructuralapproachtocontroloftransitionalwavesofnonlineardiffusionreactionsystemstheoryandpossibleapplicationstobiomedicine AT shmueleinav astructuralapproachtocontroloftransitionalwavesofnonlineardiffusionreactionsystemstheoryandpossibleapplicationstobiomedicine AT victorkardashov structuralapproachtocontroloftransitionalwavesofnonlineardiffusionreactionsystemstheoryandpossibleapplicationstobiomedicine AT shmueleinav structuralapproachtocontroloftransitionalwavesofnonlineardiffusionreactionsystemstheoryandpossibleapplicationstobiomedicine |