A note on explosion suppression for nonlinear delay differential systems by polynomial noise

References

• Appleby, J. A. D., and X. Mao. 2005. “Stochastic Stabilisation of Functional Differential Equations.” Systems & Control Letters 54 (11): 1069–1081.
   Web of Science ®Google Scholar
• Appleby, J. A. D., X. Mao, and A. Rodkina. 2008. “Stabilization and Destabilization of Nonlinear Differential Equations by Noise.” IEEE Transactions on Automatic Control 53 (3): 683–691.
   Web of Science ®Google Scholar
• Arnold, L., H. Crauel, and V. Wihstutz. 1983. “Stabilization of Linear Systems by Noise.” SIAM Journal on Control and Optimization 21 (3): 451–461.
   Web of Science ®Google Scholar
• Bahar, A., and X. Mao. 2004. “Stochastic Delay Lotka-Volterra Model.” Journal of Mathematical Analysis and Applications 292 (2): 364–380.
   Web of Science ®Google Scholar
• Chen, B., T. Jia, and Y. Niu. 2016. “Robust Fuzzy Control for Stochastic Markovian Jumping Systems via Sliding Mode Method.” International Journal of General Systems 45 (5): 604–618.
   Web of Science ®Google Scholar
• Deng, F., Q. Luo, X. Mao, and S. Pang. 2008. “Noise Suppress or Express Exponential Growth.” Systems & Control Letters 57: 262–270.
   Web of Science ®Google Scholar
• Feng, L., L. Li, and S. Zheng. 2016. “Stochastic Suppression of a Class of Functional Differential Equations.” Journal of Beijing University of Technology 42 (8): 1275–1280.
   Google Scholar
• Guo, Q., X. Mao, and R. Yue. 2016. “Almost Sure Exponential Stability of Stochastic Differential Delay Equations.” SIAM Journal on Control and Optimization 54 (4): 1919–1933.
   Web of Science ®Google Scholar
• Hu, G., M. Liu, X. Mao, and M. Song. 2009. “Noise Suppresses Exponential Growth under Regime Switching.” Journal of Mathematical Analysis and Applications 355 (2): 783–795.
   Web of Science ®Google Scholar
• Khasminskii, R. Z. 1981. Stochastic Stability of Differential Equations. Rockville: Sijthoff and Noordhoff.
   Google Scholar
• Kolmanovskii, V., and A. Myshkis. 1992. Applied Theory of Functional Differential Equations. Dordrecht/Norwell: Kluwer Academic.
   Google Scholar
• Liu, Y., F. E. Alsaadi, X. Yin, and Y. Wang. 2015. “Robust H∞ Filtering for Discrete Nonlinear Delayed Stochastic Systems with Missing Measurements and Randomly Occurring Nonlinearities.” International Journal of General Systems 44 (2): 169–181.
   Web of Science ®Google Scholar
• Liu, L., and Y. Shen. 2012. “Noise Suppresses Explosive Solutions of Differential Systems with Coefficients Satisfying the Polynomial Growth Condition.” Automatica 48 (4): 619–624.
   Web of Science ®Google Scholar
• Mao, X. 1994. Exponential Stability of Stochastic Differential Equations. New York: Dekker.
   Google Scholar
• Mao, X. 2007a. Stochastic Differential Equations and Applications. 2nd ed. Chichester: Horwood Publishing.
   Google Scholar
• Mao, X. 2007b. “Stability and Stabilisation of Stochastic Differential Delay Equations.” IET Control Theory & Applications 1 (6): 1551–1566.
   Web of Science ®Google Scholar
• Mao, X. 2016. “Almost Sure Exponential Stabilization by Discrete-time Stochastic Feedback Control.” IEEE Transactions on Automatic Control 61 (6): 1619–1624.
   Web of Science ®Google Scholar
• Mao, X., G. Marion, and E. Renshaw. 2002. “Environmental Noise Suppresses Explosion in Population Dynamics.” Stochastic Processes and their Applications 97: 95–110.
   Web of Science ®Google Scholar
• Mao, X., C. Yuan, and J. Zou. 2005. “Stochastic Differential Delay Equations of Population Dynamics.” Journal of Mathematical Analysis and Applications 304 (1): 296–320.
   Web of Science ®Google Scholar
• Sakthivel, R., M. Rathika, and M. Malik. 2017. “Robust Reliable Control of Uncertain Nonlinear Stochastic Systems Subject to Actuator Fault.” International Journal of General Systems 46 (1): 1–26.
   Web of Science ®Google Scholar
• Shen, Y., and J. Wang. 2007. “Noise-induced Stabilization of the Recurrent Neural Networks with Mixed Time-varying Delays and Markovian-switching Parameters.” IEEE Transactions on Neural Networks 18 (6): 1857–1862.
   Web of Science ®Google Scholar
• Song, Y., Q. Yin, Y. Shen, and G. Wang. 2013. “Stochastic Suppression and Stabilization of Nonlinear Differential Systems with General Decay Rate.” Journal of the Franklin Institute 350 (8): 2084–2095.
   Web of Science ®Google Scholar
• Song, S., and Q. Zhu. 2015. “Noise suppresses Explosive Solutions of Differential Systems: A New General Polynomial Growth Condition.” Journal of Mathematical Analysis and Applications 431 (1): 648–661.
   Web of Science ®Google Scholar
• Wu, F., and S. Hu. 2009. “Suppression and Stabilisation of Noise.” International Journal of Control 82: 2150–2157.
   Web of Science ®Google Scholar
• Wu, F., and S. Hu. 2011. “Stochastic Suppression and Stabilization of Delay Differential Systems.” International Journal of Robust and Nonlinear Control 21: 488–500.
   Web of Science ®Google Scholar
• Yang, Q., S. Zhu, and W. Luo. 2016. “Noise Expresses Exponential Decay for Globally Exponentially Stable Nonlinear Time Delay Systems.” Journal of The Franklin Institute 353 (9): 2074–2086.
   Web of Science ®Google Scholar
• Yin, R., Q. Zhu, Y. Shen, and S. Hu. 2016. “The Asymptotic Properties of the Suppressed Functional Differential System by Brownian Noise under Regime Switching.” International Journal of Control 89 (11): 2227–2239.
   Web of Science ®Google Scholar
• Zhu, S., Y. Shen, and G. Chen. 2010. “Noise Suppress or Express Exponential Growth for Hybrid Hopfield Neural Networks.” Physics Letters A 374 (19): 2035–2043.
   Web of Science ®Google Scholar
• Zhu, S., Q. Yang, and Y. Shen. 2016. “Noise Further Expresses Exponential Decay for Globally Exponentially Stable Time-varying Delayed Neural Networks.” Neural Networks 77: 7–13.
   PubMed Web of Science ®Google Scholar