This paper is concerned with the asymptotic behavior of solutions for a class of non-autonomous fractional FitzHugh-Nagumo equations deriven by additive white noise. We first provide some sufficient conditions for the...This paper is concerned with the asymptotic behavior of solutions for a class of non-autonomous fractional FitzHugh-Nagumo equations deriven by additive white noise. We first provide some sufficient conditions for the existence and uniqueness of solutions, and then prove the existence and uniqueness of tempered pullback random attractors for the random dynamical system generated by the solutions of considered equations in an appropriate Hilbert space. The proof is based on the uniform estimates and the decomposition of dynamical system.展开更多
Sufficient conditions for the exponential stability of a class of nonlinear, non-autonomous stochastic differential equations in infinite dimensions are studied. The analysis consists of introducing a suitable approxi...Sufficient conditions for the exponential stability of a class of nonlinear, non-autonomous stochastic differential equations in infinite dimensions are studied. The analysis consists of introducing a suitable approximating solution systems and usig a limiting argument to pass on stability of strong solutions to mild ones. Consequently, under these conditions the random attractors of given stochastic systems are reduced to zero with exponential decay. Lastly, two examples are investigated to illustrate the theory.展开更多
We investigate stochastic resonance （SR） in the FitzHugh-Nagumo system under combined bounded noise and weak harmonic excitation. Taking a spectral amplification factor as a signal-to-noise ratio, we show numericall...We investigate stochastic resonance （SR） in the FitzHugh-Nagumo system under combined bounded noise and weak harmonic excitation. Taking a spectral amplification factor as a signal-to-noise ratio, we show numerically that bounded noise can induce SR by adjusting either the intensity of bounded noise or its colour. Moreover, the increase of noise colour can enhance the SR and make the peak of the SR shift toward lower noise intensities, which is more feasible in practice. Since bounded noise is flexible to model random excitation, these findings may have some potential applications in engineering, neuroscience and biology.展开更多
The current paper is devoted to the study of the stochastic stability of FitzHugh-Nagumo systems perturbed by Gaussian white noise. First, the dynamics of stochastic FitzHugh-Nagumo systems are studied. Then, the exis...The current paper is devoted to the study of the stochastic stability of FitzHugh-Nagumo systems perturbed by Gaussian white noise. First, the dynamics of stochastic FitzHugh-Nagumo systems are studied. Then, the existence and uniqueness of their invariant measures, which mix exponentially are proved. Finally, the asymptotic behaviors of invariant measures when size of noise gets to zero are investigated.展开更多
This paper considers the dynamical behavior of solutions for non-autonomous stochastic fractional Ginzburg–Landau equations driven by additive noise with α∈(0, 1). First, we give some conditions for bounding the fr...This paper considers the dynamical behavior of solutions for non-autonomous stochastic fractional Ginzburg–Landau equations driven by additive noise with α∈(0, 1). First, we give some conditions for bounding the fractal dimension of a random invariant set of non-autonomous random dynamical system. Second, we derive uniform estimates of solutions and establish the existence and uniqueness of tempered pullback random attractors for the equation in H. At last, we prove the finiteness of fractal dimension of random attractors.展开更多
The current paper is devoted to the study of stochastic stability of FitzHugh-Nagumo systems in infinite lattice perturbed by Gaussian white noise. We first study the dynamics of stochastic FitzHugh-Nagumo systems, th...The current paper is devoted to the study of stochastic stability of FitzHugh-Nagumo systems in infinite lattice perturbed by Gaussian white noise. We first study the dynamics of stochastic FitzHugh-Nagumo systems, then prove the existence and uniqueness of their equilibriums, which mix exponentially. Finally, we investigate asymptotic behavior of equilibriums when the size of noise gets to zero.展开更多
The regularity of random attractors is considered for the non-autonomous fractional stochastic FitzHugh-Nagumo system.We prove that the system has a pullback random attractor that is compact in Hs(R^(n))×L^(2)(R^...The regularity of random attractors is considered for the non-autonomous fractional stochastic FitzHugh-Nagumo system.We prove that the system has a pullback random attractor that is compact in Hs(R^(n))×L^(2)(R^(n))and attracts all tempered random sets of L^(2)(R^(n))×L^(2)(R^(n))in the topology of Hs(R^(n))×L^(2)(R^(n))with s∈(0,1).By the idea of positive and negative truncations,spectral decomposition in bounded domains,and tail estimates,we achieved the desired results.展开更多
文摘This paper is concerned with the asymptotic behavior of solutions for a class of non-autonomous fractional FitzHugh-Nagumo equations deriven by additive white noise. We first provide some sufficient conditions for the existence and uniqueness of solutions, and then prove the existence and uniqueness of tempered pullback random attractors for the random dynamical system generated by the solutions of considered equations in an appropriate Hilbert space. The proof is based on the uniform estimates and the decomposition of dynamical system.
文摘Sufficient conditions for the exponential stability of a class of nonlinear, non-autonomous stochastic differential equations in infinite dimensions are studied. The analysis consists of introducing a suitable approximating solution systems and usig a limiting argument to pass on stability of strong solutions to mild ones. Consequently, under these conditions the random attractors of given stochastic systems are reduced to zero with exponential decay. Lastly, two examples are investigated to illustrate the theory.
基金Project supported by the Postdoctoral Fellow Grant Project (G-YX0Y) at the Hong Kong Polytechnic Universitythe National Natural Science Foundation of China (Grant No. 10872165)
文摘We investigate stochastic resonance （SR） in the FitzHugh-Nagumo system under combined bounded noise and weak harmonic excitation. Taking a spectral amplification factor as a signal-to-noise ratio, we show numerically that bounded noise can induce SR by adjusting either the intensity of bounded noise or its colour. Moreover, the increase of noise colour can enhance the SR and make the peak of the SR shift toward lower noise intensities, which is more feasible in practice. Since bounded noise is flexible to model random excitation, these findings may have some potential applications in engineering, neuroscience and biology.
基金Project supported by the National Natural Science Foundation of China(No.10926096)
文摘The current paper is devoted to the study of the stochastic stability of FitzHugh-Nagumo systems perturbed by Gaussian white noise. First, the dynamics of stochastic FitzHugh-Nagumo systems are studied. Then, the existence and uniqueness of their invariant measures, which mix exponentially are proved. Finally, the asymptotic behaviors of invariant measures when size of noise gets to zero are investigated.
基金Supported by National Natural Science Foundation of China(Grant Nos.11571245,11771444,11871138 and11871049)funding of V.C.&V.R.Key Lab of Sichuan Province+2 种基金the Yue Qi Young Scholar ProjectChina University of Mining and Technology(Beijing)China Scholarship Council(CSC)。
文摘This paper considers the dynamical behavior of solutions for non-autonomous stochastic fractional Ginzburg–Landau equations driven by additive noise with α∈(0, 1). First, we give some conditions for bounding the fractal dimension of a random invariant set of non-autonomous random dynamical system. Second, we derive uniform estimates of solutions and establish the existence and uniqueness of tempered pullback random attractors for the equation in H. At last, we prove the finiteness of fractal dimension of random attractors.
基金Supported by National Natural Science Foundation of China （Grant Nos. 10926096, 10971225）
文摘The current paper is devoted to the study of stochastic stability of FitzHugh-Nagumo systems in infinite lattice perturbed by Gaussian white noise. We first study the dynamics of stochastic FitzHugh-Nagumo systems, then prove the existence and uniqueness of their equilibriums, which mix exponentially. Finally, we investigate asymptotic behavior of equilibriums when the size of noise gets to zero.
基金This work was partially supported by the National Natural Science Foundation of China(Grant Nos.11771444,11871138)the Yue Qi Young Scholar Project+3 种基金China University of Mining and Technology(Beijing),China Scholarship Council(CSC)the Funding of V.C.&V.R.Key Lab of Sichuan Provincethe Funding of Young Backbone Teacher in Henan ProvinceHenan Overseas Expertise Introduction Center for Discipline Innovation.
文摘The regularity of random attractors is considered for the non-autonomous fractional stochastic FitzHugh-Nagumo system.We prove that the system has a pullback random attractor that is compact in Hs(R^(n))×L^(2)(R^(n))and attracts all tempered random sets of L^(2)(R^(n))×L^(2)(R^(n))in the topology of Hs(R^(n))×L^(2)(R^(n))with s∈(0,1).By the idea of positive and negative truncations,spectral decomposition in bounded domains,and tail estimates,we achieved the desired results.
