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Dynamics of some stochastic chemostat models with multiplicative noise

Communications on Pure and Applied Analysis  Volume 16, Issue 5, Pages : 1893 - 1914, 2017

Tomás Caraballo - (email), María J. Garrido–Atienza - (email), J. López-de-la-Cruz - (email)

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2

A mathematical model for the seasonal transmission of schistosomiasis in the lake and marshland regions of China

Mathematical Biosciences and Engineering  Volume 14, Issue 5/6, Pages : 1279 - 1299, 2017

Yingke Li - (email), Zhidong Teng - (email), Shigui Ruan - (email), Mingtao Li - (email), Xiaomei Feng - (email)

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3

Transition of interaction outcomes in a facilitation-competition system of two species

Mathematical Biosciences and Engineering  Volume 14, Issue 5/6, Pages : 1463 - 1475, 2017

Yuanshi Wang - (email), Hong Wu - (email)

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4

Asymptotic behavior of a delayed stochastic logistic model with impulsive perturbations

Mathematical Biosciences and Engineering  Volume 14, Issue 5/6, Pages : 1477 - 1498, 2017

Sanling Yuan - (email), Xuehui Ji - (email), Huaiping Zhu - (email)

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5

Extinction in stochastic predator-prey population model with Allee effect on prey

Discrete and Continuous Dynamical Systems - Series B  Volume 22, Issue 7, Pages : 2651 - 2667, 2017

Miljana Jovanović - (email), Marija Krstić - (email)

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6

Adaptive methods for stochastic differential equations via natural embeddings and rejection sampling with memory

Discrete and Continuous Dynamical Systems - Series B  Volume 22, Issue 7, Pages : 2731 - 2761, 2017

Christopher Rackauckas - (email), Qing Nie - (email)

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7

Stationarity and periodicity of positive solutions to stochastic SEIR epidemic models with distributed delay

Discrete and Continuous Dynamical Systems - Series B  Volume 22, Issue 6, Pages : 2479 - 2500, 2017

Qun Liu - (email), Daqing Jiang - (email), Ningzhong Shi - (email), Tasawar Hayat - (email), Ahmed Alsaedi - (email)

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8

Instantaneous shrinking and extinction for a non-Newtonian polytropic filtration equation with orientated convection

Discrete and Continuous Dynamical Systems - Series B  Volume 22, Issue 4, Pages : 1743 - 1755, 2017

Hailong Ye - (email), Jingxue Yin - (email)

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9

Population dynamical behavior of a two-predator one-prey stochastic model with time delay

Discrete and Continuous Dynamical Systems  Volume 37, Issue 5, Pages : 2513 - 2538, 2017

Meng Liu - (email), Chuanzhi Bai - (email), Yi Jin - (email)

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10

Persistence and stationary distribution of a stochastic predator-prey model under regime switching

Discrete and Continuous Dynamical Systems  Volume 37, Issue 5, Pages : 2881 - 2897, 2017

Li Zu - (email), Daqing Jiang - (email), Donal O'Regan - (email)

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11

A sustainability condition for stochastic forest model

Communications on Pure and Applied Analysis  Volume 16, Issue 2, Pages : 699 - 718, 2017

Tôn Viêt Ta - (email), Linh Thi Hoai Nguyen - (email), Atsushi Yagi - (email)

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12

Extinction and uniform strong persistence of a size-structured population model

Discrete and Continuous Dynamical Systems - Series B  Volume 22, Issue 3, Pages : 831 - 840, 2016

Keng Deng - (email), Yixiang Wu - (email)

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13

Long-time behavior of an SIR model with perturbed disease transmission coefficient

Discrete and Continuous Dynamical Systems - Series B  Volume 21, Issue 10, Pages : 3429 - 3440, 2016

Nguyen Huu Du - (email), Nguyen Thanh Dieu - (email)

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14

A comparison between random and stochastic modeling for a SIR model

Communications on Pure and Applied Analysis  Volume 16, Issue 1, Pages : 151 - 162, 2016

Tomás Caraballo - (email), Renato Colucci - (email)

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15

On the mathematical modelling of tumor-induced angiogenesis

Mathematical Biosciences and Engineering  Volume 14, Issue 1, Pages : 45 - 66, 2016

Luis L. Bonilla - (email), Vincenzo Capasso - (email), Mariano Alvaro - (email), Manuel Carretero - (email), Filippo Terragni - (email)

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16

Newton's method for nonlinear stochastic wave equations driven by one-dimensional Brownian motion

Mathematical Biosciences and Engineering  Volume 14, Issue 1, Pages : 237 - 248, 2016

Henryk Leszczyński - (email), Monika Wrzosek - (email)

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17

An integral inequality for the invariant measure of some finite dimensional stochastic differential equation

Discrete and Continuous Dynamical Systems - Series B  Volume 21, Issue 9, Pages : 3015 - 3027, 2016

Giuseppe Da Prato - (email)

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18

Stochastic models in biology and the invariance problem

Discrete and Continuous Dynamical Systems - Series B  Volume 21, Issue 7, Pages : 2145 - 2168, 2016

Jacky Cresson - (email), Bénédicte Puig - (email), Stefanie Sonner - (email)

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19

A nonlocal sample dependence SDE-PDE system modeling proton dynamics in a tumor

Discrete and Continuous Dynamical Systems - Series B  Volume 21, Issue 7, Pages : 2233 - 2254, 2016

Peter E. Kloeden - (email), Stefanie Sonner - (email), Christina Surulescu - (email)

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20

Kolmogorov-type systems with regime-switching jump diffusion perturbations

Discrete and Continuous Dynamical Systems - Series B  Volume 21, Issue 7, Pages : 2293 - 2319, 2016

Fuke Wu - (email), George Yin - (email), Zhuo Jin - (email)

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21

Analysis of a non-autonomous mutualism model driven by Levy jumps

Discrete and Continuous Dynamical Systems - Series B  Volume 21, Issue 4, Pages : 1189 - 1202, 2016

Mei Li - (email), Hongjun Gao - (email), Bingjun Wang - (email)

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22

Approximation of the first passage time density of a Wiener process to an exponentially decaying boundary by two-piecewise linear threshold. Application to neuronal spiking activity

Mathematical Biosciences and Engineering  Volume 13, Issue 3, Pages : 613 - 629, 2016

Massimiliano Tamborrino - (email)

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23

Optimal layer reinsurance on the maximization of the adjustment coefficient

Numerical Algebra, Control and Optimization  Volume 6, Issue 1, Pages : 21 - 34, 2016

Xuepeng Zhang - (email), Zhibin Liang - (email)

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24

Stability of interacting traveling waves in reaction-convection-diffusion systems

DCDS Supplements  Volume 2015, Issue special, Pages : 258 - 266, 2015

Grigori Chapiro - (email), Lucas Furtado - (email), Dan Marchesin - (email), Stephen Schecter - (email)

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25

Persistence-time estimation for some stochastic SIS epidemic models

Discrete and Continuous Dynamical Systems - Series B  Volume 20, Issue 9, Pages : 2933 - 2947, 2015

Francisco de la Hoz - (email), Anna Doubova - (email), Fernando Vadillo - (email)

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26

Dynamics of a host-pathogen system on a bounded spatial domain

Communications on Pure and Applied Analysis  Volume 14, Issue 6, Pages : 2535 - 2560, 2015

Feng-Bin Wang - (email), Junping Shi - (email), Xingfu Zou - (email)

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27

Balancing survival and extinction in nonautonomous competitive Lotka-Volterra systems with infinite delays

Discrete and Continuous Dynamical Systems - Series B  Volume 20, Issue 8, Pages : 2663 - 2690, 2015

Francisco Montes de Oca - (email), Liliana Pérez - (email)

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28

Stochastic averaging for slow-fast dynamical systems with fractional Brownian motion

Discrete and Continuous Dynamical Systems - Series B  Volume 20, Issue 7, Pages : 2257 - 2267, 2015

Yong Xu - (email), Bin Pei - (email), Rong Guo - (email)

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29

Extinction in discrete, competitive, multi-species patch models

Discrete and Continuous Dynamical Systems - Series B  Volume 20, Issue 6, Pages : 1583 - 1590, 2015

David M. Chan - (email), Matt McCombs - (email), Sarah Boegner - (email), Hye Jin Ban - (email), Suzanne L. Robertson - (email)

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30

Stability and persistence in ODE models for populations with many stages

Mathematical Biosciences and Engineering  Volume 12, Issue 4, Pages : 661 - 686, 2015

Guihong Fan - (email), Yijun Lou - (email), Horst R. Thieme - (email), Jianhong Wu - (email)

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31

Robust output stabilization for a class of nonlinear uncertain stochastic systems under multiplicative and additive noises: The attractive ellipsoid method

Journal of Industrial and Management Optimization  Volume 12, Issue 1, Pages : 169 - 186, 2015

Hussain Alazki - (email), Alexander Poznyak - (email)

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32

Dynamics of a parasite-host epidemiological model in spatial heterogeneous environment

Discrete and Continuous Dynamical Systems - Series B  Volume 20, Issue 4, Pages : 989 - 1013, 2015

Yongli Cai - (email), Weiming Wang - (email)

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33

Global dynamics and traveling wave solutions of two predators-one prey models

Discrete and Continuous Dynamical Systems - Series B  Volume 20, Issue 4, Pages : 1135 - 1154, 2015

Jian-Jhong Lin - (email), Weiming Wang - (email), Caidi Zhao - (email), Ting-Hui Yang - (email)

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34

The threshold of a stochastic SIRS epidemic model in a population with varying size

Discrete and Continuous Dynamical Systems - Series B  Volume 20, Issue 4, Pages : 1277 - 1295, 2015

Yanan Zhao - (email), Daqing Jiang - (email), Xuerong Mao - (email), Alison Gray - (email)

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35

Dragging in mutualistic networks

Networks and Heterogeneous Media  Volume 10, Issue 1, Pages : 37 - 52, 2015

Juan Manuel Pastor - (email), Javier García-Algarra - (email), José M. Iriondo - (email), José J. Ramasco - (email), Javier Galeano - (email)

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36

A simple and bounded model of population dynamics for mutualistic networks

Networks and Heterogeneous Media  Volume 10, Issue 1, Pages : 53 - 70, 2015

Juan Manuel Pastor - (email), Javier García-Algarra - (email), Javier Galeano - (email), José María Iriondo - (email), José J. Ramasco - (email)

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37

Optimal harvesting for a stochastic N-dimensional competitive Lotka-Volterra model with jumps

Discrete and Continuous Dynamical Systems - Series B  Volume 20, Issue 2, Pages : 683 - 701, 2015

Xiaoling Zou - (email), Ke Wang - (email)

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38

The stability of a perturbed eco-epidemiological model with Holling type II functional response by white noise

Discrete and Continuous Dynamical Systems - Series B  Volume 20, Issue 1, Pages : 295 - 321, 2014

Qiumei Zhang - (email), Daqing Jiang - (email), Li Zu - (email)

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39

A counterexample to finite time stopping property for one-harmonic map flow

Communications on Pure and Applied Analysis  Volume 14, Issue 1, Pages : 121 - 125, 2014

Yoshikazu Giga - (email), Hirotoshi Kuroda - (email)

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40

Modeling colony collapse disorder in honeybees as a contagion

Mathematical Biosciences and Engineering  Volume 11, Issue 6, Pages : 1275 - 1294, 2014

Christopher M. Kribs-Zaleta - (email), Christopher Mitchell - (email)

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41

Discontinuity waves as tipping points: Applications to biological & sociological systems

Discrete and Continuous Dynamical Systems - Series B  Volume 19, Issue 7, Pages : 1911 - 1934, 2014

John Bissell - (email), Brian Straughan - (email)

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42

The transition point in the zero noise limit for a 1D Peano example

Discrete and Continuous Dynamical Systems  Volume 34, Issue 10, Pages : 4071 - 4083, 2014

François Delarue - (email), Franco Flandoli - (email)

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43

Stochastic averaging principle for dynamical systems with fractional Brownian motion

Discrete and Continuous Dynamical Systems - Series B  Volume 19, Issue 4, Pages : 1197 - 1212, 2014

Yong Xu - (email), Rong Guo - (email), Di Liu - (email), Huiqing Zhang - (email), Jinqiao Duan - (email)

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44

Critical transitions in a model of a genetic regulatory system

Mathematical Biosciences and Engineering  Volume 11, Issue 4, Pages : 723 - 740, 2014

Jesse Berwald - (email), Marian Gidea - (email)

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45

$R_0$ and the global behavior of an age-structured SIS epidemic model with periodicity and vertical transmission

Mathematical Biosciences and Engineering  Volume 11, Issue 4, Pages : 929 - 945, 2014

Toshikazu Kuniya - (email), Mimmo Iannelli - (email)

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46

Stochastic dynamics of SIRS epidemic models with random perturbation

Mathematical Biosciences and Engineering  Volume 11, Issue 4, Pages : 1003 - 1025, 2014

Qingshan Yang - (email), Xuerong Mao - (email)

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47

Stability and optimal control for some classes of tritrophic systems

Mathematical Biosciences and Engineering  Volume 11, Issue 2, Pages : 257 - 283, 2013

Luca Galbusera - (email), Sara Pasquali - (email), Gianni Gilioli - (email)

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48

On the dynamics of two-consumers-one-resource competing systems with Beddington-DeAngelis functional response

Discrete and Continuous Dynamical Systems - Series B  Volume 18, Issue 9, Pages : 2331 - 2353, 2013

Sze-Bi Hsu - (email), Shigui Ruan - (email), Ting-Hui Yang - (email)

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49

Traveling wave solutions for a diffusive sis epidemic model

Discrete and Continuous Dynamical Systems - Series B  Volume 18, Issue 5, Pages : 1291 - 1304, 2013

Wei Ding - (email), Wenzhang Huang - (email), Siroj Kansakar - (email)

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50

Khasminskii-type theorems for stochastic functional differential equations

Discrete and Continuous Dynamical Systems - Series B  Volume 18, Issue 6, Pages : 1697 - 1714, 2013

Minghui Song - (email), Liangjian Hu - (email), Xuerong Mao - (email), Liguo Zhang - (email)

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51

Population dynamical behavior of Lotka-Volterra cooperative systems with random perturbations

Discrete and Continuous Dynamical Systems  Volume 33, Issue 6, Pages : 2495 - 2522, 2012

Meng Liu - (email), Ke Wang - (email)

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52

Basic stochastic models for viral infection within a host

Mathematical Biosciences and Engineering  Volume 9, Issue 4, Pages : 915 - 935, 2012

Sukhitha W. Vidurupola - (email), Linda J. S. Allen - (email)

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53

Stochastic models for competing species with a shared pathogen

Mathematical Biosciences and Engineering  Volume 9, Issue 3, Pages : 461 - 485, 2012

Linda J. S. Allen - (email), Vrushali A. Bokil - (email)

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54

Regularity of $\infty$ for elliptic equations with measurable coefficients and its consequences

Discrete and Continuous Dynamical Systems  Volume 32, Issue 10, Pages : 3379 - 3397, 2012

Ugur G. Abdulla - (email)

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Coexistence and extinction in the Volterra-Lotka competition model with nonlocal dispersal

Communications on Pure and Applied Analysis  Volume 11, Issue 5, Pages : 1699 - 1722, 2012

Georg Hetzer - (email), Tung Nguyen - (email), Wenxian Shen - (email)

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56

Front propagation in diffusion-aggregation models with bi-stable reaction

Discrete and Continuous Dynamical Systems - Series B  Volume 16, Issue 3, Pages : 819 - 833, 2011

Mikhail Kuzmin - (email), Stefano Ruggerini - (email)

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57

Fluctuation and extinction dynamics in host-microparasite systems

Communications on Pure and Applied Analysis  Volume 10, Issue 5, Pages : 1537 - 1548, 2011

Kaifa Wang - (email), Yang Kuang - (email)

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58

Global dynamics of the periodic un-stirred chemostat with a toxin-producing competitor

Communications on Pure and Applied Analysis  Volume 9, Issue 6, Pages : 1639 - 1651, 2010

Yifu Wang - (email), Jingxue Yin - (email)

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Beyond multiscale and multiphysics: Multimaths for model coupling

Networks and Heterogeneous Media  Volume 5, Issue 3, Pages : 423 - 460, 2010

Xavier Blanc - (email), Claude Le Bris - (email), Frédéric Legoll - (email), Tony Lelièvre - (email)

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60

Analysis of a predator-prey model with predators impulsively diffusing between two patches

Discrete and Continuous Dynamical Systems - Series B  Volume 14, Issue 3, Pages : 1081 - 1094, 2010

Jianjun Jiao - (email), Lansun Chen - (email)

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Rational exemption to vaccination for non-fatal SIS diseases: Globally stable and oscillatory endemicity

Mathematical Biosciences and Engineering  Volume 7, Issue 3, Pages : 561 - 578, 2010

Bruno Buonomo - (email), Alberto d’Onofrio - (email), Deborah Lacitignola - (email)

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62

Stochastic Lotka-Volterra system with unbounded distributed delay

Discrete and Continuous Dynamical Systems - Series B  Volume 14, Issue 1, Pages : 275 - 288, 2010

Fuke Wu - (email), Yangzi Hu - (email)

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63

Dynamics of a plant-herbivore model with toxin-induced functional response

Mathematical Biosciences and Engineering  Volume 7, Issue 1, Pages : 149 - 169, 2010

Ya Li - (email), Z. Feng - (email)

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Accurate parameter estimation for coupled stochastic dynamics

DCDS Supplements  Volume 2009, Issue Special, Pages : 44 - 53, 2009

Robert Azencott - (email), Yutheeka Gadhyan - (email)

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65

A mathematical model of an Agricultural-Industrial-Ecospheric system with industrial competition

Communications on Pure and Applied Analysis  Volume 8, Issue 5, Pages : 1689 - 1707, 2009

Ibrahim Agyemang - (email), H. I. Freedman - (email)

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Population dynamical behavior of non-autonomous Lotka-Volterra competitive system with random perturbation

Discrete and Continuous Dynamical Systems  Volume 24, Issue 2, Pages : 523 - 545, 2009

Xiaoyue Li - (email), Xuerong Mao - (email)

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67

Global dynamics of a Predator-Prey model with Hassell-Varley Type functional response

Discrete and Continuous Dynamical Systems - Series B  Volume 10, Issue 4, Pages : 857 - 871, 2008

Sze-Bi Hsu - (email), Tzy-Wei Hwang - (email), Yang Kuang - (email)

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Reaction-diffusion equations for population dynamics with forced speed I - The case of the whole space

Discrete and Continuous Dynamical Systems  Volume 21, Issue 1, Pages : 41 - 67, 2008

Henri Berestycki - (email), Luca Rossi - (email)

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69

Generators of Feller semigroups with coefficients depending on parameters and optimal estimators

Discrete and Continuous Dynamical Systems - Series B  Volume 8, Issue 2, Pages : 511 - 527, 2007

Jerome A. Goldstein - (email), Rosa Maria Mininni - (email), Silvia Romanelli - (email)

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70

Allee effects in a discrete-time host-parasitoid model with stage structure in the host

Discrete and Continuous Dynamical Systems - Series B  Volume 8, Issue 1, Pages : 145 - 159, 2007

S. R.-J. Jang - (email)

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71

Comparison between stochastic and deterministic selection-mutation models

Mathematical Biosciences and Engineering  Volume 4, Issue 2, Pages : 133 - 157, 2007

Azmy S. Ackleh - (email), Shuhua Hu - (email)

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72

Stochastic epidemic models with a backward bifurcation

Mathematical Biosciences and Engineering  Volume 3, Issue 3, Pages : 445 - 458, 2006

Linda J. S. Allen - (email), P. van den Driessche - (email)

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73

On stochastic stabilization of difference equations

Discrete and Continuous Dynamical Systems  Volume 15, Issue 3, Pages : 843 - 857, 2006

John A. D. Appleby - (email), Xuerong Mao - (email), Alexandra Rodkina - (email)

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Pathwise non-exponential decay rates of solutions of scalar nonlinear stochastic differential equations

Discrete and Continuous Dynamical Systems - Series B  Volume 6, Issue 4, Pages : 667 - 696, 2006

John A. D. Appleby - (email), Alexandra Rodkina - (email), Henri Schurz - (email)

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On the stochastic Burgers equation with a polynomial nonlinearity in the real line

Discrete and Continuous Dynamical Systems - Series B  Volume 6, Issue 4, Pages : 835 - 866, 2006

Jong Uhn Kim - (email)

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Stochastic Galerkin method for elliptic spdes: A white noise approach

Discrete and Continuous Dynamical Systems - Series B  Volume 6, Issue 4, Pages : 941 - 955, 2006

Luis J. Roman - (email), Marcus Sarkis - (email)

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Dissipation of mean energy of discretized linear oscillators under random perturbations

DCDS Supplements  Volume 2005, Issue Special, Pages : 778 - 783, 2005

Henri Schurz - (email)

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78

Permanence of predator-prey system with stage structure

Discrete and Continuous Dynamical Systems - Series B  Volume 4, Issue 3, Pages : 547 - 554, 2004

Jing-An Cui - (email), Xinyu Song - (email)

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Coexistence in a metapopulation model with explicit local dynamics

Mathematical Biosciences and Engineering  Volume 1, Issue 1, Pages : 131 - 145, 2004

Zhilan Feng - (email), Robert Swihart - (email), Yingfei Yi - (email), Huaiping Zhu - (email)

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Stochastic modeling of carcinogenesis: State space models and estimation of parameters

Discrete and Continuous Dynamical Systems - Series B  Volume 4, Issue 1, Pages : 297 - 322, 2003

W. Y. Tan - (email), L.-J. Zhang - (email), C.W. Chen - (email)

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The problem Of blow-up in nonlinear parabolic equations

Discrete and Continuous Dynamical Systems  Volume 8, Issue 2, Pages : 399 - 433, 2002

Victor A. Galaktionov - (email), Juan-Luis Vázquez - (email)

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A PDE approach to stochastic invariance

Discrete and Continuous Dynamical Systems  Volume 6, Issue 3, Pages : 651 - 664, 2000

Hitoshi Ishii - (email), Paola Loreti - (email), Maria Elisabetta Tessitore - (email)

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