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2007, Encyclopedia of mathematics and its applications, ISBN 9780521879897, Volume 113, xii, 419
Recent years have seen an explosion of interest in stochastic partial differential equations where the driving noise is discontinuous. In this comprehensive... 
Lévy processes | Stochastic partial differential equations | Laevy processes | Levy processes
Book
Journal of Mathematical Analysis and Applications, ISSN 0022-247X, 02/2014, Volume 410, Issue 2, pp. 750 - 763
This paper is concerned with stochastic Lotka–Volterra models perturbed by Lévy noise. Firstly, stochastic logistic models with Lévy noise are investigated.... 
Persistence | Lévy noise | Extinction | Lotka–Volterra model | Lotka-Volterra model | MATHEMATICS | Levy noise | MATHEMATICS, APPLIED | BEHAVIOR | MODEL | POPULATION-DYNAMICS | RANDOM PERTURBATION | JUMPS | Analysis | Extinction (Biology)
Journal Article
Chaos, Solitons and Fractals: the interdisciplinary journal of Nonlinear Science, and Nonequilibrium and Complex Phenomena, ISSN 0960-0779, 10/2019, Volume 127, pp. 118 - 126
In this paper, the dynamical behavior of simplified FitzHugh-Nagumo (FHN) neuron system under the co-excitation of Lévy noise and Gaussian white noise are... 
Lévy noise | First-passage time | FHN neural system | Resonance activation | Noise enhanced stability | BISTABLE KINETIC-MODEL | PHYSICS, MULTIDISCIPLINARY | MEAN 1ST-PASSAGE TIME | STATE | SUPPRESSION | PHYSICS, MATHEMATICAL | Levy noise | MATHEMATICS, INTERDISCIPLINARY APPLICATIONS | STOCHASTIC RESONANCE
Journal Article
Physics Letters A, ISSN 0375-9601, 07/2016, Volume 380, Issue 33, pp. 2485 - 2488
Transport of overdamped particle driven by a colored Lévy noise in a static ratchet potential is investigated. We analyze the influence of the noise in the... 
Colored Lévy noise | Current inversion | Ratchet potential | Lévy flight | Levy flight | RATCHETS | MODELS | PHYSICS, MULTIDISCIPLINARY | EXTERNAL FORCE-FIELDS | ORNSTEIN-UHLENBECK | FLIGHTS | Colored Levy noise | Competition | Correlation | Noise | Breaking | Inversions | Solid state physics | Mathematical models | Transport
Journal Article
International Journal of Modern Physics B, ISSN 0217-9792, 11/2018, Volume 32, Issue 28, p. 1850313
In this paper, the Lévy noise-induced transition in an underdamped asymmetric bistable system is discussed. Lévy noise is generated  through the Janicki–Weron... 
Lévy noise | stationary probability density | noise-induced transition | underdamped asymmetric bistable system | Levy noise | PHYSICS, CONDENSED MATTER | ACTIVATION | PHYSICS, APPLIED | DYNAMICS | WHITE-NOISE | POTENTIALS | PHYSICS, MATHEMATICAL | STOCHASTIC RESONANCE
Journal Article
Journal of Mathematical Analysis and Applications, ISSN 0022-247X, 07/2012, Volume 391, Issue 2, pp. 363 - 375
This paper considers stochastic population dynamics driven by Lévy noise. The contributions of this paper lie in that: (a) Using the Khasminskii–Mao theorem,... 
Brownian motion | Pathwise estimation | Lévy noise | Exponential martingale inequality with jumps | MATHEMATICS | Levy noise | MATHEMATICS, APPLIED | LOTKA-VOLTERRA MODEL | DIFFERENTIAL-DELAY EQUATIONS | JUMPS
Journal Article
International Journal of Control, ISSN 0020-7179, 08/2017, Volume 90, Issue 8, pp. 1703 - 1712
Journal Article
Journal of Theoretical Biology, ISSN 0022-5193, 11/2019, Volume 480, pp. 166 - 174
This paper considers about the escape paths of the FitzHugh–Nagumo neural system driven by symmetric -stable Lévy noise (non-Gaussian noise). The existing... 
Non-Gaussian Lévy motion | Probability density function | Stochastic dynamics | Fitzhugh–Nagumo model | Maximal likely trajectory | Fitzhugh-Nagumo model | PATH | Non-Gaussian Levy motion | BIOLOGY | MATHEMATICAL & COMPUTATIONAL BIOLOGY | COHERENCE RESONANCE | STOCHASTIC RESONANCE
Journal Article
Systems & Control Letters, ISSN 0167-6911, 08/2018, Volume 118, pp. 62 - 68
Journal Article
Physica A: Statistical Mechanics and its Applications, ISSN 0378-4371, 04/2018, Volume 495, pp. 294 - 311
This paper concerns the dynamics of a stochastic predator–prey system with Markovian switching and Lévy noise. First, the existence and uniqueness of global... 
Markov chain | Beddington–DeAngelis | Predator–prey | Lévy noise | Stochastic permanence | LESLIE-GOWER | PHYSICS, MULTIDISCIPLINARY | EQUATIONS | Beddington-DeAngelis | RANDOM PERTURBATION | Levy noise | LOTKA-VOLTERRA MODEL | Predator-prey | DIFFUSION | POPULATION-DYNAMICS | EXTINCTION | JUMPS | Markov processes | Information science | Analysis
Journal Article
Journal of Physics A: Mathematical and Theoretical, ISSN 1751-8113, 01/2017, Volume 50, Issue 3, p. 34003
We investigate the stochastic dynamics of an active particle moving at a constant speed under the influence of a fluctuating torque. In our model the angular... 
α-stable noise | Lévy noise | active particles | Fickian diffusion | Ornstein Uhlenbeck process | nongaussian displacement | BROWNIAN-MOTION | PHYSICS, MULTIDISCIPLINARY | BEHAVIOR | PHYSICS, MATHEMATICAL | Levy noise | PERSISTENT TURNING WALKER | alpha-stable noise | DYNAMICS | MOVEMENT | non-gaussian displacement | ZIGZAG COURSE
Journal Article
Advances in Difference Equations, ISSN 1687-1839, 12/2018, Volume 2018, Issue 1, pp. 1 - 21
Journal Article
Physica A: Statistical Mechanics and its Applications, ISSN 0378-4371, 07/2018, Volume 502, pp. 492 - 505
This work is concerned with a three-species stochastic delay prey–mesopredator–superpredator system with Lévy noise. We will characterize the complete dynamic... 
Prey–mesopredator–superpredator model | Lévy noise | Stability | Extinction | Levy noise | PHYSICS, MULTIDISCIPLINARY | POPULATION SYSTEMS | DYNAMICS | DIFFERENTIAL-EQUATIONS | MODEL | Prey-mesopredator-superpredator model | JUMPS | Analysis | Population biology | Extinction (Biology)
Journal Article
Computers and Mathematics with Applications, ISSN 0898-1221, 03/2019, Volume 77, Issue 6, pp. 1503 - 1512
In this work we study a stochastic three-dimensional Landau–Lifshitz–Gilbert equation with non-zero anisotropy energy, which is drive by pure jump noise. We... 
Weak martingale solutions | Marcus canonical form | Lévy noise | Stochastic Landau–Lifshitz equation | Levy noise | MATHEMATICS, APPLIED | Stochastic Landau-Lifshitz equation | Anisotropy | Galerkin method | Martingales
Journal Article
Physica A: Statistical Mechanics and its Applications, ISSN 0378-4371, 10/2014, Volume 411, pp. 95 - 103
Journal Article
Physica A: Statistical Mechanics and its Applications, ISSN 0378-4371, 10/2013, Volume 392, Issue 20, pp. 4739 - 4748
In this paper, we investigate stochastic bifurcation for a tumor–immune system in the presence of a symmetric non-Gaussian Lévy noise. Stationary probability... 
Stochastic bifurcation | Tumor–immune system | Lévy noise | Tumor-immune system | Levy noise | ENVIRONMENTS | RESONANCE | PHYSICS, MULTIDISCIPLINARY | BISTABILITY | NON-GAUSSIAN NOISES | GROWTH | VARIABLES | MODEL | Analysis | Tumors | Immune system
Journal Article
Journal of Mathematical Analysis and Applications, ISSN 0022-247X, 08/2014, Volume 416, Issue 1, pp. 126 - 142
This paper is devoted to study a class of stochastic differential equations with Lévy noise. In comparison to the standard Gaussian noise, Lévy noise is more... 
Continuous in probability | Lévy noise | Asymptotic stability in the pth moment | Almost sure stability | Continuous in the pth moment | Stochastic differential equation | MATHEMATICS | Levy noise | MATHEMATICS, APPLIED | Parathyroid hormone | Analysis | Differential equations
Journal Article
中国科学:技术科学英文版, ISSN 1674-7321, 2016, Volume 59, Issue 3, pp. 371 - 375
This paper aims to investigate the stochastic resonance (SR) in an FitzHugh-Nagumo (FHN) model with an additive LEvy noise numerically. The non-Gaussian LEvy... 
随机波动 | 高斯噪声 | 随机共振 | 模型 | 共振现象 | 诱导 | 数值模拟 | 随机噪声 | Engineering | stochastic resonance | Lévy noise | Engineering, general | FHN model | signal-to-noise ratio | SYSTEM | CRAYFISH | SIGNAL | Levy noise | ENGINEERING, MULTIDISCIPLINARY | MATERIALS SCIENCE, MULTIDISCIPLINARY | DRIVEN | BIFURCATION
Journal Article
Advances in Difference Equations, ISSN 1687-1839, 12/2018, Volume 2018, Issue 1, pp. 1 - 16
Journal Article
Physica A: Statistical Mechanics and its Applications, ISSN 0378-4371, 10/2019, Volume 531, p. 121747
The effects of non-Gaussian Lévy noise in a competitive neural model of binocular rivalry are analyzed numerically. We first investigate how Lévy noise added... 
Winner-take-all | Lévy noise | Alternation | Mean dominance duration | Adaptation process | Levy noise | DOMINANCE | PHYSICS, MULTIDISCIPLINARY | ORNSTEIN-UHLENBECK | FREQUENCY | DYNAMICS | RIVALRY | NEURAL MODEL
Journal Article