Generalised theory on asymptotic stability and boundedness of stochastic functional differential equations [PDF]
, 2011 Asymptotic stability and boundedness have been two of most popular topics in the study of stochastic functional differential equations (SFDEs) (see e.g. Appleby and Reynolds (2008), Appleby and Rodkina (2009), Basin and Rodkina (2008), Khasminskii (1980),
Luo, Qi, Shen, Yi, Mao, Xuerong
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Uniformly Ultimate Boundedness Control with Decentralized Event-Triggering [PDF]
, 2021 Event-triggered control is a method that the control input is updated only when a certain condition is satisfied (i.e., an event occurs). In this paper, event-triggered control over a sensor network is studied based on the notion of uniformly ultimate ...
Yamashita, Yuh +2 more
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Risk-Aware Stability, Ultimate Boundedness, and Positive Invariance [PDF]
, 2022 This paper introduces the notions of stability, ultimate boundedness, and positive invariance for stochastic systems in the view of risk. More specifically, those notions are defined in terms of the worst-case Conditional Value-at-Risk (CVaR), which ...
Kishida, Masako
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New result on the ultimate boundedness of solutions of certain third-order vector differential equations [PDF]
, 1983 summary:Sufficient conditions are established for ultimate boundedness of solutions of certain nonlinear vector differential equations of third-order. Our result improves on Tunc’s [C.
Fatmi, Larbi +6 more
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Ultimate boundedness of some third order ordinary differential equations [PDF]
, 2012 summary:We prove the ultimate boundedness of solutions of some third order nonlinear ordinary differential equations using the Lyapunov method. The results obtained generalize earlier results of Ezeilo, Tejumola, Reissig, Tunç and others.
Afuwape, Anthony Uyi, Omeike, M. O.
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Stochastic Delay Population Dynamics under Regime Switching: Global Solutions and Extinction
Abstract and Applied Analysis, 2013 This paper is concerned with a delay Lotka-Volterra model under regime switching diffusion in random environment. By using generalized Itô formula, Gronwall inequality and Young’s inequality, some sufficient conditions for existence of global positive ...
Zheng Wu, Hao Huang, Lianglong Wang
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LG–Holling type II diseased predator ecosystem with Lévy noise and white noise
Advances in Difference Equations, 2018 This paper considers an LG–Holling type II diseased predator ecosystem with Lévy noise and white noise. In this prey–predator system, assuming that the predator population is infected by disease and divided into two classes: susceptible predator and ...
Shuang Li
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Dynamical Behavior of a Stochastic Ratio-Dependent Predator-Prey System
Journal of Applied Mathematics, 2012 This paper is concerned with a stochastic ratio-dependent predator-prey model with varible coefficients. By the comparison theorem of stochastic equations and the Itô formula, the global existence of a unique positive solution of the ratio-dependent ...
Zheng Wu, Hao Huang, Lianglong Wang
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Asymptotic properties of a stochastic Lotka–Volterra model with infinite delay and regime switching
Advances in Difference Equations, 2018 We investigate the long-term properties of a stochastic Lotka–Volterra model with infinite delay and Markovian chains on a finite state space. We investigate that the stochastic model admits a unique positive global solution which stays in the way of ...
Qingteng Lin +3 more
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Uniformly ultimate boundedness of solutions for some 3-dimensional systems [PDF]
, 2004 For some 3-dimensional system of electrial circuits, the uniformly ultimate boundedness of solutions is proved, and consequently existing unstable manifolds around equilibrium points is ...
Nakajima, Fumio
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