Action potential-like modes as modulated waves in an extended soliton model for biomembranes and nerves
By extending the Heimburg–Jackson soliton model for neural signals that considers the effects of higher-order nonlinearities, the dynamics of modulated waves characterizing electromechanical density pulses is described in the form of soliton-like pulse signals representing nerve impulses, well-known...
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AIP Publishing LLC
2025-01-01
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| Series: | AIP Advances |
| Online Access: | http://dx.doi.org/10.1063/5.0233543 |
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| author | J. A. Onana Inouga S. E. Mkam Tchouobiap M. Siewe Siewe F. M. Moukam Kakmeni |
| author_facet | J. A. Onana Inouga S. E. Mkam Tchouobiap M. Siewe Siewe F. M. Moukam Kakmeni |
| author_sort | J. A. Onana Inouga |
| collection | DOAJ |
| description | By extending the Heimburg–Jackson soliton model for neural signals that considers the effects of higher-order nonlinearities, the dynamics of modulated waves characterizing electromechanical density pulses is described in the form of soliton-like pulse signals representing nerve impulses, well-known as action potential pulses (Appulses). The investigation is performed both analytically and numerically, where a comprehensive picture of higher-order nonlinearities effects on the generation and evolution of nerve impulses is provided. Within the framework of a multiple-scale-expansion analysis and the reductive perturbation method, while considering third- and fourth-order nonlinearities, the electromechanical area-density pulse propagation is investigated, leading to the generation of a localized Appulse. Accordingly, the analytical theory uses a perturbative technique, and a damped cubic–quintic nonlinear Schrödinger equation is derived, which admits a single-pulse-type solitary solution that possesses different phase characteristics of the typical neuronal Appulse structure, representative of nerve impulse profiles. A modulational instability (MI) analysis demonstrates the increase of the modulation gain in the system with increasing fourth-order nonlinearity, indicating that the higher-order nonlinearities influence the MI in the proposed extended soliton model. Furthermore, a numerical analysis is performed, and consistent agreement with the analytical prediction is achieved, confirming a localized typical longitudinal single pulse-like solitary wave solution for the extended soliton model. Importantly, the appearance of a typical longitudinal single-solitary pulse-type structure can evolve uniformly with increasing fourth-order nonlinearity, leading to the splitting of the single-pulse-soliton signal and resulting in the appearance of a double asymmetric localized pulse-like mode or bisoliton-pulse structure, characteristic of a coupled Appulse. |
| format | Article |
| id | doaj-art-ace7380125fa44548a9a3a4bd288e025 |
| institution | Kabale University |
| issn | 2158-3226 |
| language | English |
| publishDate | 2025-01-01 |
| publisher | AIP Publishing LLC |
| record_format | Article |
| series | AIP Advances |
| spelling | doaj-art-ace7380125fa44548a9a3a4bd288e0252025-02-03T16:40:42ZengAIP Publishing LLCAIP Advances2158-32262025-01-01151015035015035-1910.1063/5.0233543Action potential-like modes as modulated waves in an extended soliton model for biomembranes and nervesJ. A. Onana InougaS. E. Mkam Tchouobiap0M. Siewe Siewe1F. M. Moukam Kakmeni2Complex Systems and Theoretical Biology Group, Laboratory of Research on Advanced Materials and Nonlinear Science (LaRAMaNS), Department of Physics, Faculty of Science, University of Buea, P.O. Box 63, Buea, CameroonLaboratory of Mechanics, Materials and Structures, Department of Physics, Faculty of Science, University of Yaounde I, P.O. Box 812, Yaounde, CameroonComplex Systems and Theoretical Biology Group, Laboratory of Research on Advanced Materials and Nonlinear Science (LaRAMaNS), Department of Physics, Faculty of Science, University of Buea, P.O. Box 63, Buea, CameroonBy extending the Heimburg–Jackson soliton model for neural signals that considers the effects of higher-order nonlinearities, the dynamics of modulated waves characterizing electromechanical density pulses is described in the form of soliton-like pulse signals representing nerve impulses, well-known as action potential pulses (Appulses). The investigation is performed both analytically and numerically, where a comprehensive picture of higher-order nonlinearities effects on the generation and evolution of nerve impulses is provided. Within the framework of a multiple-scale-expansion analysis and the reductive perturbation method, while considering third- and fourth-order nonlinearities, the electromechanical area-density pulse propagation is investigated, leading to the generation of a localized Appulse. Accordingly, the analytical theory uses a perturbative technique, and a damped cubic–quintic nonlinear Schrödinger equation is derived, which admits a single-pulse-type solitary solution that possesses different phase characteristics of the typical neuronal Appulse structure, representative of nerve impulse profiles. A modulational instability (MI) analysis demonstrates the increase of the modulation gain in the system with increasing fourth-order nonlinearity, indicating that the higher-order nonlinearities influence the MI in the proposed extended soliton model. Furthermore, a numerical analysis is performed, and consistent agreement with the analytical prediction is achieved, confirming a localized typical longitudinal single pulse-like solitary wave solution for the extended soliton model. Importantly, the appearance of a typical longitudinal single-solitary pulse-type structure can evolve uniformly with increasing fourth-order nonlinearity, leading to the splitting of the single-pulse-soliton signal and resulting in the appearance of a double asymmetric localized pulse-like mode or bisoliton-pulse structure, characteristic of a coupled Appulse.http://dx.doi.org/10.1063/5.0233543 |
| spellingShingle | J. A. Onana Inouga S. E. Mkam Tchouobiap M. Siewe Siewe F. M. Moukam Kakmeni Action potential-like modes as modulated waves in an extended soliton model for biomembranes and nerves AIP Advances |
| title | Action potential-like modes as modulated waves in an extended soliton model for biomembranes and nerves |
| title_full | Action potential-like modes as modulated waves in an extended soliton model for biomembranes and nerves |
| title_fullStr | Action potential-like modes as modulated waves in an extended soliton model for biomembranes and nerves |
| title_full_unstemmed | Action potential-like modes as modulated waves in an extended soliton model for biomembranes and nerves |
| title_short | Action potential-like modes as modulated waves in an extended soliton model for biomembranes and nerves |
| title_sort | action potential like modes as modulated waves in an extended soliton model for biomembranes and nerves |
| url | http://dx.doi.org/10.1063/5.0233543 |
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