1 |
R. Z. Khas'minskii, Necessary and Sufficient Conditions for the Asymptotic Stability of Linear Stochastic Systems, Theory of Probability and its Applications 12 (1967), no. 1, 144-147.
DOI
|
2 |
C. Luo and S. Guo, Stability and Bifurcation of Two-dimensional Stochastic Differential Equations with Multiplicative Excitations, Bull. Malays. Math. Sci. Soc. 40 (2017), no. 2, 795-817.
DOI
|
3 |
X. Mao, Stochastic differential equations and applications, Woodhead Publishing, UK, 2007.
|
4 |
C. Rocsoreanu, A. Georgescu, and N. Giurgiteanu, The FitzHugh Nagumo model: Bifurcations and Dynamics, Kluver Academic Publishers Boston, 2000.
|
5 |
M. E. Yamakou, T. D. Tran, L. H. Duc, and J. M. Jost, Stochastic FitzHugh-Nagumo neuron model in excitable regime embeds a leaky integrate-and-fire model, Journal of Mathematical Biology 79 (2019) 509-532.
DOI
|
6 |
U. Wagner and W. V. Weding, On the calculation of stationary solutions of multidimensional Fokker-Planck equation by orthogonal function, Nonlinear Dynamics 29 (2000), 283-306.
|
7 |
N. Berglund and D. Landon, Mixed-mode oscillations and interspike interval statistics in the stochastic FitzHugh-Nagumo model, Nonlinearity 25 (2012), no. 8, 2303-2335.
DOI
|
8 |
D. Brown, J. Feng, and S. Feerick, Variability of firing of Hodgkin-Huxley and FitzHughNagumo neurons with stochastic synaptic input, Phys. Rev. Lett. 82 (1999), no. 7, 4731-4734.
DOI
|
9 |
T. Caraballo, J. A. Langa, and J. C. Robinson, A stochastic pitchfork bifurcation in a reaction-diffusion equation, Proceedings Mathematical Physical and Engineering Sciences 457 (2013), no. 2013, 2041-2061.
|
10 |
L. Arnold, Random Dynamical Systems. Berlin, Springer, 2007.
|
11 |
S. R. D. Dtchetgnia, R. Yamapi, T. C. Kofane, and M. A. Aziz-Alaoui, Deterministic and Stochastic Bifurcations in the Hindmarsh-Rose neuronal Model, Chaos 23 (2013), no. 3, 033125.
DOI
|
12 |
B. Ermentrout, Type I membranes, phase resetting curves, and synchrony, Neural Comput. 8 (1996), no. 5, 979-1001.
DOI
|
13 |
A. Hodgkin and A. Huxley, A quantitative description of membrane current and application to conduction and excitation in nerve, The Journal of Physiology 117 (1952), no. 4, 500-544.
DOI
|
14 |
E. M. Izhikevich, Dynamical Systems in Neuroscience: The Geometry of Excitability and Bursting, The MIT Press, 2007.
|
15 |
C. Laing and G. J. Lord, Stochastic Methods in neuroscience. Clarendon Press. Oxford, 2008.
|
16 |
Y. Liang and N. S. Namachchivaya, P-Bifurcations in the Noisy Duffing-van der Pol Equation, Stochastic Dynamics. (Bremen, 1997), 49-70, Springer, New York, 1999.
|
17 |
M. Ringqvist, On Dynamical Behaviour of FitzHugh-Nagumo Systems, Filosofie licentiatavhandling, 2006.
|
18 |
J. H. Yang, Miguel A.F. Sanju'an, H. G. Liu, and X. Li, Stochastic P-bifurcation and stochastic resonance in a noisy bistable fractional-order system, Commun Nonlinear Sci Numer Simulat. 41 (2016), 104-117 .
DOI
|
19 |
M. H. Akrami and M. Fatehi Nia, Stochastic Stability and Bifurcation for the Selkov Model with Noise, Iranian Journal of Mathematical Chemistry 12 (2021), no.1, 39-55.
|
20 |
M. Fatehi Nia and M. H. Akrami, Stability and bifurcation in a stochastic vocal folds model, Communications in Nonlinear Science and Numerical Simula- tion 79, (2019), 104898.
DOI
|
21 |
N. Berglund and B. Gentz, Pathwise description of dynamic pitchfork bifurcations with additive noise, Probability Theory and Related Fields 122 (2002), 341-388.
DOI
|
22 |
S. Bonaccorsi and E. Mastrogiacomo, Analysis of the stochastic FitzHugh-Nagumo system, Infin. Dimens. Anal. Quantum Probab. Relat. Top. 11 (2008), no. 3, 427-446.
DOI
|
23 |
S. Chakraborty, S. Pal, and N. Bairagi, Predator-prey fishery model under deterministic and stochastic environments: a mathematical perspective, International Journal of Dynamical Systems and Differential Equations 4 (2012), no. 3, 215-241.
DOI
|