Otwarty dostęp

Pitchfork bifurcation and vibrational resonance in a neutral delayed system

   | 15 lut 2024

Zacytuj

Wang, H., Ma, J., Chen, Y., et al. (2014). Effect of an autapse on the firing pattern transition in a bursting neuron. Communications in Nonlinear Science and Numerical Simulation, 19(9), 3242-3254. https://doi.org/10.1016/j.cnsns.2014.02.018 Search in Google Scholar

Qin, H., Ma, J., Jin, W., et al. (2014). Dynamics of electric activities in neuron and neurons of network induced by autapses. Science China Technological Sciences, 57, 936-946. https://doi.org/10.1007/s11431-014-5534-0 Search in Google Scholar

Sun, J., & Ding, Q. (2013). Advances in analysis and control of time-delayed dynamical systems. Higher Education Press. (in Chinese) Search in Google Scholar

Verdugo, A., & Rand, R. (2008). Hopf bifurcation in a DDE model of gene expression. Communications in Nonlinear Science and Numerical Simulation, 13(2), 235-242. https://doi.org/10.1016/j.cnsns.2006.05.001 Search in Google Scholar

Wu, F., & Xu, Y. (2009). Stochastic Lotka-Volterra population dynamics with infinite delay. SIAM Journal on Applied Mathematics, 70(3), 641-657. https://doi.org/10.1137/080719194 Search in Google Scholar

Hu, Y. (in Chinese). Stability Study of Neutral Delay Systems. University of Science and Technology of China. Search in Google Scholar

Yang, J., Sanjuán, M. A. F., & Liu, H. (2015). Signal generation and enhancement in a delayed system. Communications in Nonlinear Science & Numerical Simulation, 22(1-3), 1158-1168. https://doi.org/10.1016/j.cnsns.2014.08.005 Search in Google Scholar

Daqaq, M. F., Alhazza, K. A., & Qaroush, Y. (2011). On primary resonances of weakly nonlinear delay systems with cubic nonlinearities. Nonlinear Dynamics, 64, 253-277. https://doi.org/10.1007/s11071-010-9859-3 Search in Google Scholar

Saeed, N. A., El-Ganini, W. A., & Eissa, M. (2013). Nonlinear time delay saturation-based controller for suppression of nonlinear beam vibrations. Applied Mathematical Modelling, 37(20-21), 8846-8864. https://doi.org/10.1016/j.apm.2013.04.010 Search in Google Scholar

Maccari, A. (2003). Vibration control for the primary resonance of a cantilever beam by a time delay state feedback. Journal of Sound and Vibration, 259(2), 241-251. https://doi.org/10.1006/jsvi.2002.5144 Search in Google Scholar

Yang, J., & Liu, X. (2010). Delay induces quasi-periodic vibrational resonance. Journal of Physics A: Mathematical and Theoretical, 43(12), 122001. https://doi.org/10.1088/1751-8113/43/12/122001 Search in Google Scholar

Jeevarathinam, C., Rajasekar, S., & Sanjuán, M. A. F. (2011). Theory and numerics of vibrational resonance in Duffing oscillators with time-delayed feedback. Physical Review E, 83(6), 066205. https://doi.org/10.1103/PhysRevE.83.066205 Search in Google Scholar

Yang, J., & Zhu, H. (2013). Bifurcation and resonance induced by fractional-order damping and time delay feedback in a Duffing system. Communications in Nonlinear Science and Numerical Simulation, 18(5), 1316-1326. https://doi.org/10.1016/j.cnsns.2012.09.023 Search in Google Scholar

Yang, J., Sanjuán, M. A. F., Xiang, W., et al. (2013). Pitchfork bifurcation and vibrational resonance in a fractional-order Duffing oscillator. Pramana, 81, 943-957. https://doi.org/10.1007/s12043-013-0621-5 Search in Google Scholar

Yang, J., & Liu, X. (2012). Analysis of periodic vibrational resonance induced by linear time delay feedback. Acta Physica Sinica, 61(1), 010505. (in Chinese) https://doi.org/10.7498/aps.61.010505 Search in Google Scholar

Gammaitoni, L., Hänggi, P., Jung, P., et al. (1998). Stochastic resonance. Reviews of Modern Physics, 70(1), 223. https://doi.org/10.1103/RevModPhys.70.223 Search in Google Scholar

Landa, P. S., & McClintock, P. V. E. (2000). Vibrational resonance. Journal of Physics A: Mathematical and General, 33(45), L433-L438. https://doi.org/10.1088/0305-4470/33/45/103 Search in Google Scholar

Baltanás, J. P., Lopez, L., Blechman, I. I., et al. (2003). Experimental evidence, numerics, and theory of vibrational resonance in bistable systems. Physical Review E, 67(6), 066119. https://doi.org/10.1103/PhysRevE.67.066119 Search in Google Scholar

Xiao, L., Zhang, X., Lu, S., et al. (2019). A novel weak-fault detection technique for rolling element bearing based on vibrational resonance. Journal of Sound and Vibration, 438, 490-505. https://doi.org/10.1016/j.jsv.2018.09.039 Search in Google Scholar

Ge, M., Lu, L., Xu, Y., et al. (2020). Vibrational mono-/bi-resonance and wave propagation in FitzHugh Nagumo neural systems under electromagnetic induction. Chaos, Solitons & Fractals, 133, 109645. https://doi.org/10.1016/j.chaos.2020.109645 Search in Google Scholar

Ren, Y., Pan, Y., Duan, F., et al. (2017). Exploiting vibrational resonance in weak-signal detection. Physical Review E, 96(2), 022141. https://doi.org/10.1103/PhysRevE.96.022141 Search in Google Scholar

Calderón, L. F., Chuang, C., & Brumer, P. (2023). Electronic vibrational resonance does not significantly alter steady-state transport in natural light-harvesting systems. The Journal of Physical Chemistry Letters, 14(6), 1436-1444. https://doi.org/10.1021/acs.jpclett.2c03842 Search in Google Scholar

Huang, S., Zhang, J., Yang, J., et al. (2023). Logical vibrational resonance in a symmetric bistable system: Numerical and experimental studies. Communications in Nonlinear Science and Numerical Simulation, 119, 107123. https://doi.org/10.1016/j.cnsns.2023.107123 Search in Google Scholar

Jeevarathinam, C., Rajasekar, S., & Sanjuán, M. A. F. (2013). Effect of multiple time-delay on vibrational resonance. Chaos: An Interdisciplinary Journal of Nonlinear Science, 23(1), 013136. https://doi.org/10.1063/1.4793542 Search in Google Scholar

Xie, J., Guo, R., Ren, Z., He, D., & Xu, H. (2023). Vibration resonance and fork bifurcation of under-damped Duffing system with fractional and linear delay terms. Nonlinear Dynamics, 111, 10981-10999. https://doi.org/10.1007/s11071-023-08462-2 Search in Google Scholar

Yan, Z., & Liu, X. (2021). Fractional-order harmonic resonance in a multi-frequency excited fractional Duffing oscillator with distributed time delay. Communications in Nonlinear Science and Numerical Simulation, 97, 105754. https://doi.org/10.1016/j.cnsns.2021.105754 Search in Google Scholar

Ning, L., & Chen, Z. (2020). Vibrational resonance analysis in a gene transcriptional regulatory system with two different forms of time-delays. Physica D: Nonlinear Phenomena, 401, 132164. https://doi.org/10.1016/j.physd.2019.132164 Search in Google Scholar

Wang, R., Zhang, H., & Zhang, Y. (2022). Bifurcation and vibration resonance in the time delay Duffing system with fractional internal and external damping. Meccanica, 57(5), 999-1015. https://doi.org/10.1007/s11012-022-01483-y Search in Google Scholar

Guo, W., & Ning, L. (2020). Vibrational resonance in a fractional order quintic oscillator system with time delay feedback. International Journal of Bifurcation and Chaos, 30(02), 2050025. https://doi.org/10.1142/S021812742050025X Search in Google Scholar

Li, R., Li, J., & Huang, D. (2021). Static bifurcation and vibrational resonance in an asymmetric fractional-order delay duffing system. Physica Scripta, 96(8), 085214. https://doi.org/10.1088/1402-4896/ac00e6 Search in Google Scholar

Blekhman, I. I. (2004). Selected Topics in Vibrational Mechanics. Singapore: World Scientific. Search in Google Scholar

Thomsen, J. J. (2021). Vibrations and Stability: Advanced Theory, Analysis, and Tools. Berlin: Springer. Search in Google Scholar

Guckenheimer, J., & Holmes, P. (2013). Nonlinear Oscillations, Dynamical Systems, and Bifurcations of Vector Fields. New York: Springer-Verlag. Search in Google Scholar

eISSN:
2444-8656
Język:
Angielski
Częstotliwość wydawania:
Volume Open
Dziedziny czasopisma:
Life Sciences, other, Mathematics, Applied Mathematics, General Mathematics, Physics