Melnikov-type method and homoclinic bifurcation in a class of hybrid piecewise smooth systems under noise and impulsive excitation
In this paper, we developed the classical Melnikov method in a class of general hybrid abstract piecewise smooth systems subjected to elastic and rigid impact effects under noise and impulsive excitation. The relevant unperturbed Hamiltonian systems possess the homoclinic orbit and tristable charact...
| প্রধান লেখক: | , , |
|---|---|
| বিন্যাস: | Journal article |
| ভাষা: | English |
| প্রকাশিত: |
Springer
2025
|
| _version_ | 1826317810883624960 |
|---|---|
| author | Li, Y Wei, Z Moroz, I |
| author_facet | Li, Y Wei, Z Moroz, I |
| author_sort | Li, Y |
| collection | OXFORD |
| description | In this paper, we developed the classical Melnikov method in a class of general hybrid abstract piecewise smooth systems subjected to elastic and rigid impact effects under noise and impulsive excitation. The relevant unperturbed Hamiltonian systems possess the homoclinic orbit and tristable characteristic. The homoclinic orbit will continuously cross the first two switching manifolds, jump across the third one subjected to the impulsive excitation, then jump about the x-axis on the fourth and last one symmetrically due to the rigid impact effect, but won’t cross the last one in the existence of the corresponding unilateral rigid constraint. Specifically, the perturbed trajectories will jump across the first switching manifold by the reset mapping rule about the elastic impact effect. Moreover, our new random Melnikov-type process and function will be got, the criteria of homoclinic chaos about the systems without or with noise excitation can also be obtained. Finally, the homoclinic bifurcation and chaos about a concrete hybrid seven-piecewise feedback control system under saturation and dead zone constrains are analysed and verified through our extended Melnikov-type method and numerical simulations. |
| first_indexed | 2025-03-11T16:59:49Z |
| format | Journal article |
| id | oxford-uuid:b69f9fdc-af8e-4caa-8aeb-21e3e2fa4a58 |
| institution | University of Oxford |
| language | English |
| last_indexed | 2025-03-11T16:59:49Z |
| publishDate | 2025 |
| publisher | Springer |
| record_format | dspace |
| spelling | oxford-uuid:b69f9fdc-af8e-4caa-8aeb-21e3e2fa4a582025-03-10T11:39:56ZMelnikov-type method and homoclinic bifurcation in a class of hybrid piecewise smooth systems under noise and impulsive excitationJournal articlehttp://purl.org/coar/resource_type/c_dcae04bcuuid:b69f9fdc-af8e-4caa-8aeb-21e3e2fa4a58EnglishSymplectic ElementsSpringer2025Li, YWei, ZMoroz, IIn this paper, we developed the classical Melnikov method in a class of general hybrid abstract piecewise smooth systems subjected to elastic and rigid impact effects under noise and impulsive excitation. The relevant unperturbed Hamiltonian systems possess the homoclinic orbit and tristable characteristic. The homoclinic orbit will continuously cross the first two switching manifolds, jump across the third one subjected to the impulsive excitation, then jump about the x-axis on the fourth and last one symmetrically due to the rigid impact effect, but won’t cross the last one in the existence of the corresponding unilateral rigid constraint. Specifically, the perturbed trajectories will jump across the first switching manifold by the reset mapping rule about the elastic impact effect. Moreover, our new random Melnikov-type process and function will be got, the criteria of homoclinic chaos about the systems without or with noise excitation can also be obtained. Finally, the homoclinic bifurcation and chaos about a concrete hybrid seven-piecewise feedback control system under saturation and dead zone constrains are analysed and verified through our extended Melnikov-type method and numerical simulations. |
| spellingShingle | Li, Y Wei, Z Moroz, I Melnikov-type method and homoclinic bifurcation in a class of hybrid piecewise smooth systems under noise and impulsive excitation |
| title | Melnikov-type method and homoclinic bifurcation in a class of hybrid piecewise smooth systems under noise and impulsive excitation |
| title_full | Melnikov-type method and homoclinic bifurcation in a class of hybrid piecewise smooth systems under noise and impulsive excitation |
| title_fullStr | Melnikov-type method and homoclinic bifurcation in a class of hybrid piecewise smooth systems under noise and impulsive excitation |
| title_full_unstemmed | Melnikov-type method and homoclinic bifurcation in a class of hybrid piecewise smooth systems under noise and impulsive excitation |
| title_short | Melnikov-type method and homoclinic bifurcation in a class of hybrid piecewise smooth systems under noise and impulsive excitation |
| title_sort | melnikov type method and homoclinic bifurcation in a class of hybrid piecewise smooth systems under noise and impulsive excitation |
| work_keys_str_mv | AT liy melnikovtypemethodandhomoclinicbifurcationinaclassofhybridpiecewisesmoothsystemsundernoiseandimpulsiveexcitation AT weiz melnikovtypemethodandhomoclinicbifurcationinaclassofhybridpiecewisesmoothsystemsundernoiseandimpulsiveexcitation AT morozi melnikovtypemethodandhomoclinicbifurcationinaclassofhybridpiecewisesmoothsystemsundernoiseandimpulsiveexcitation |