
Previous Article
On the behaviour at infinity of solutions to stationary convectiondiffusion equation in a cylinder
 DCDSB Home
 This Issue

Next Article
Relaxation oscillation profile of limit cycle in predatorprey system
Constrained stability and instability of polynomial difference equations with statedependent noise
1.  Department of Mathematics, University of the West Indies, Kingston, 7, Jamaica, Jamaica 
However, for any fixed initial value, the probability of instability is nonzero, and in fact we can show that as the magnitude of the initial value increases, the probability of instability approaches $1$.
[1] 
Eugen Stumpf. Local stability analysis of differential equations with statedependent delay. Discrete & Continuous Dynamical Systems  A, 2016, 36 (6) : 34453461. doi: 10.3934/dcds.2016.36.3445 
[2] 
Tomás Caraballo, Leonid Shaikhet. Stability of delay evolution equations with stochastic perturbations. Communications on Pure & Applied Analysis, 2014, 13 (5) : 20952113. doi: 10.3934/cpaa.2014.13.2095 
[3] 
Leonid Shaikhet. Stability of delay differential equations with fading stochastic perturbations of the type of white noise and poisson's jumps. Discrete & Continuous Dynamical Systems  B, 2020, 25 (9) : 36513657. doi: 10.3934/dcdsb.2020077 
[4] 
Gregory Berkolaiko, Cónall Kelly, Alexandra Rodkina. Sharp pathwise asymptotic stability criteria for planar systems of linear stochastic difference equations. Conference Publications, 2011, 2011 (Special) : 163173. doi: 10.3934/proc.2011.2011.163 
[5] 
Jan Čermák, Jana Hrabalová. Delaydependent stability criteria for neutral delay differential and difference equations. Discrete & Continuous Dynamical Systems  A, 2014, 34 (11) : 45774588. doi: 10.3934/dcds.2014.34.4577 
[6] 
Ferenc Hartung, Janos Turi. Linearized stability in functional differential equations with statedependent delays. Conference Publications, 2001, 2001 (Special) : 416425. doi: 10.3934/proc.2001.2001.416 
[7] 
Ismael Maroto, Carmen Núñez, Rafael Obaya. Exponential stability for nonautonomous functional differential equations with statedependent delay. Discrete & Continuous Dynamical Systems  B, 2017, 22 (8) : 31673197. doi: 10.3934/dcdsb.2017169 
[8] 
LaSu Mai, Kaijun Zhang. Asymptotic stability of steady state solutions for the relativistic EulerPoisson equations. Discrete & Continuous Dynamical Systems  A, 2016, 36 (2) : 9811004. doi: 10.3934/dcds.2016.36.981 
[9] 
István Györi, Ferenc Hartung. Exponential stability of a statedependent delay system. Discrete & Continuous Dynamical Systems  A, 2007, 18 (4) : 773791. doi: 10.3934/dcds.2007.18.773 
[10] 
Saroj P. Pradhan, Janos Turi. Parameter dependent stability/instability in a human respiratory control system model. Conference Publications, 2013, 2013 (special) : 643652. doi: 10.3934/proc.2013.2013.643 
[11] 
Andrejs Reinfelds, Klara Janglajew. Reduction principle in the theory of stability of difference equations. Conference Publications, 2007, 2007 (Special) : 864874. doi: 10.3934/proc.2007.2007.864 
[12] 
Jitai Liang, Ben Niu, Junjie Wei. Linearized stability for abstract functional differential equations subject to statedependent delays with applications. Discrete & Continuous Dynamical Systems  B, 2019, 24 (11) : 61676188. doi: 10.3934/dcdsb.2019134 
[13] 
Tibor Krisztin. A local unstable manifold for differential equations with statedependent delay. Discrete & Continuous Dynamical Systems  A, 2003, 9 (4) : 9931028. doi: 10.3934/dcds.2003.9.993 
[14] 
Evelyn Buckwar, Girolama Notarangelo. A note on the analysis of asymptotic meansquare stability properties for systems of linear stochastic delay differential equations. Discrete & Continuous Dynamical Systems  B, 2013, 18 (6) : 15211531. doi: 10.3934/dcdsb.2013.18.1521 
[15] 
Wei Mao, Liangjian Hu, Xuerong Mao. Asymptotic boundedness and stability of solutions to hybrid stochastic differential equations with jumps and the EulerMaruyama approximation. Discrete & Continuous Dynamical Systems  B, 2019, 24 (2) : 587613. doi: 10.3934/dcdsb.2018198 
[16] 
Yoshihiro Hamaya. Stability properties and existence of almost periodic solutions of volterra difference equations. Conference Publications, 2009, 2009 (Special) : 315321. doi: 10.3934/proc.2009.2009.315 
[17] 
John A. D. Appleby, Xuerong Mao, Alexandra Rodkina. On stochastic stabilization of difference equations. Discrete & Continuous Dynamical Systems  A, 2006, 15 (3) : 843857. doi: 10.3934/dcds.2006.15.843 
[18] 
Christian Lax, Sebastian Walcher. A note on global asymptotic stability of nonautonomous master equations. Discrete & Continuous Dynamical Systems  B, 2013, 18 (8) : 21432149. doi: 10.3934/dcdsb.2013.18.2143 
[19] 
Zhong Tan, Leilei Tong. Asymptotic stability of stationary solutions for magnetohydrodynamic equations. Discrete & Continuous Dynamical Systems  A, 2017, 37 (6) : 34353465. doi: 10.3934/dcds.2017146 
[20] 
Hermann Brunner, Chunhua Ou. On the asymptotic stability of Volterra functional equations with vanishing delays. Communications on Pure & Applied Analysis, 2015, 14 (2) : 397406. doi: 10.3934/cpaa.2015.14.397 
2019 Impact Factor: 1.27
Tools
Metrics
Other articles
by authors
[Back to Top]