Ratcheting and energetic aspects of synchronization in coupled bursting neurons
In this paper, we investigate the dynamics of two coupled bursting neurons. The Hindmarsh–Rose mathematical model of the neuron subjected to an external periodic stimulus is considered. We transform this model into that of the one-dimensional problem of a particle driven by a periodic external force...
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| Veröffentlicht in: | Nonlinear dynamics 2016, Vol.83 (1-2), p.541-554 |
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| creator | Yamakou, E. Marius Inack, E. Maeva Moukam Kakmeni, F. M. |
| description | In this paper, we investigate the dynamics of two coupled bursting neurons. The Hindmarsh–Rose mathematical model of the neuron subjected to an external periodic stimulus is considered. We transform this model into that of the one-dimensional problem of a particle driven by a periodic external force under the influence of a double-well potential. We study the bifurcation structures, chaotic behavior, and the synchronization dynamics of the transformed model. Numerical simulations reveal the existence of some bifurcation structures including saddle-node, symmetry-breaking, and period-doubling route to chaos. By varying the system’s parameters, we also find thresholds for which the system remains periodic. In Lyapunov exponent diagrams, regions of chaos, quasi-periodicity, and periodicity are clearly identified. In the synchronization dynamics, the Lyapunov function criteria is used to determine the stability of the synchronized states. In addition, the threshold parameters for which the synchronization occurs have been found. The synchronization energy of the coupled model is derived using the generalized Hamiltonian formalism. It is shown that maintaining the system in a synchronized regime requires a nonzero flow of energy per unit time. |
| doi_str_mv | 10.1007/s11071-015-2346-0 |
| format | Article |
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In the synchronization dynamics, the Lyapunov function criteria is used to determine the stability of the synchronized states. In addition, the threshold parameters for which the synchronization occurs have been found. The synchronization energy of the coupled model is derived using the generalized Hamiltonian formalism. 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M.</creatorcontrib><title>Ratcheting and energetic aspects of synchronization in coupled bursting neurons</title><title>Nonlinear dynamics</title><addtitle>Nonlinear Dyn</addtitle><description>In this paper, we investigate the dynamics of two coupled bursting neurons. The Hindmarsh–Rose mathematical model of the neuron subjected to an external periodic stimulus is considered. We transform this model into that of the one-dimensional problem of a particle driven by a periodic external force under the influence of a double-well potential. We study the bifurcation structures, chaotic behavior, and the synchronization dynamics of the transformed model. Numerical simulations reveal the existence of some bifurcation structures including saddle-node, symmetry-breaking, and period-doubling route to chaos. By varying the system’s parameters, we also find thresholds for which the system remains periodic. In Lyapunov exponent diagrams, regions of chaos, quasi-periodicity, and periodicity are clearly identified. In the synchronization dynamics, the Lyapunov function criteria is used to determine the stability of the synchronized states. In addition, the threshold parameters for which the synchronization occurs have been found. The synchronization energy of the coupled model is derived using the generalized Hamiltonian formalism. It is shown that maintaining the system in a synchronized regime requires a nonzero flow of energy per unit time.</description><subject>Automotive Engineering</subject><subject>Bifurcations</subject><subject>Bursting</subject><subject>Chaos theory</subject><subject>Classical Mechanics</subject><subject>Computer simulation</subject><subject>Control</subject><subject>Dynamic stability</subject><subject>Dynamic structural analysis</subject><subject>Dynamical Systems</subject><subject>Dynamics</subject><subject>Engineering</subject><subject>Joining</subject><subject>Liapunov functions</subject><subject>Mathematical models</subject><subject>Mechanical Engineering</subject><subject>Neurons</subject><subject>Original Paper</subject><subject>Parameters</subject><subject>Periodic variations</subject><subject>Ratcheting</subject><subject>Serrated yielding</subject><subject>Synchronism</subject><subject>Synchronization</subject><subject>Vibration</subject><issn>0924-090X</issn><issn>1573-269X</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2016</creationdate><recordtype>article</recordtype><sourceid>BENPR</sourceid><recordid>eNp1kEtLAzEUhYMoWKs_wF3AjZvozWMyk6UUX1AoiEJ3IZOm7ZRpMiYzC_31po4gCK4uF77vcDgIXVK4oQDlbaIUSkqAFoRxIQkcoQktSk6YVMtjNAHFBAEFy1N0ltIOADiDaoIWL6a3W9c3foONX2HnXdzk12KTOmf7hMMapw9vtzH45tP0TfC48diGoWvdCtdDTN-yd0Mm0jk6WZs2uYufO0VvD_evsycyXzw-z-7mxHKhemKo4mVlVGFy44pTULXLfUCJUlDHOWWcSculACtrXtvaMFeaTCqrhF1JPkXXY24Xw_vgUq_3TbKubY13YUiaVjlNClawjF79QXdhiD6304wVSkgGoDJFR8rGkFJ0a93FZm_ih6agDxPrcWKdC-vDxBqyw0YnZdZvXPxN_l_6Aji6fYM</recordid><startdate>2016</startdate><enddate>2016</enddate><creator>Yamakou, E. 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| subjects | Automotive Engineering Bifurcations Bursting Chaos theory Classical Mechanics Computer simulation Control Dynamic stability Dynamic structural analysis Dynamical Systems Dynamics Engineering Joining Liapunov functions Mathematical models Mechanical Engineering Neurons Original Paper Parameters Periodic variations Ratcheting Serrated yielding Synchronism Synchronization Vibration |
| title | Ratcheting and energetic aspects of synchronization in coupled bursting neurons |
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