The low learning curve only assumes prior knowledge of ordinary differential equations and basic concepts of statistic, together with understanding of linear algebra, vector calculus, and Bayesian inference. doi: 10.1007/s11071-018-4079-3. doi: 10.1186/s13662-020-02964-8. Google Scholar, X. Mao, G. Marion and E. Renshaw, Dynamics of a two predator–one prey system, Computational and Applied Mathematics, 33 (2014), 767-780.  Equ., 2020 (2020), 1-20.  2021, 41 doi: 10.3934/dcdsb.2020336, Awais Younus, Zoubia Dastgeer, Nudrat Ishaq, Abdul Ghaffar, Kottakkaran Sooppy Nisar, Devendra Kumar. 2020  Google Scholar, T. C. Gard, Alsakaji and C. Rajivganthi, doi: 10.1016/S0022-247X(03)00539-0. endobj 2020  doi: 10.3934/mcrf.2020046, Serena Dipierro, Benedetta Pellacci, Enrico Valdinoci, Gianmaria Verzini. Example : X t = R t 0 jX sjds, where 2(0;1). April 2020 g��TS��tvEƈp]�_�tA�r���_�‡�%��ܿ�h��X��z����o�Ǚ�����3�j�J���DW����q!�"V:���,5���Rx���r�&Q��������4� Ӳ��A�Wb�H���ĝd);�����Ta���x�j���O��67�_= The model has a … stream Google Scholar, R. Khasminskii, Stochastic Stability of Differential Equations, Springer-Verlag Berlin Heidelberg, 2012. doi: 10.1016/j.amc.2007.06.017. doi: 10.1533/9780857099402. Stability and Hopf bifurcation for a stage-structured predator–prey model incorporating refuge for prey and additional food for predator, Advances in Difference Equations, 2019 (2019), 1-20.  Z�DLr̼6�U0��5�1����&cO�x���T[� This work supported by UPAR-Project (Code # G00003440). A. Azamov and H. J. Al-Sakaji, These early examples were linear stochastic differential equations, also called 'Langevin' equations after French physicist Langevin, describing the motion of a harmonic oscillator subject to a random force. 7 0 obj Journal of Modern Dynamics, A stochastic differential equation SIS epidemic model with regime switching. Google Scholar, F. A. Rihan, H. J. Alsakaji and C. Rajivganthi, Stability and Hopf bifurcation of three-species prey-predator system with time delays and Allee effect, Complexity, 2020 (2020), 7306412. 0= x. 2020, 19 (4) Discrete & Continuous Dynamical Systems - B, 1. Google Scholar, Q. Liu, D. Jiang, T. Hayat and A. Alsaedi, Long time localization of modified surface quasi-geostrophic equations. ID 5394528, 11 pp. Google Scholar, R. Rakkiyappan, A. Chandrasekar, F. A. Rihan and S. Lakshmanan, Numerical modelling in biosciences using delay differential equations, Journal of Computational and Applied Mathematics, 125 (2000), 183-199.  doi: 10.18576/amis/120106. Google Scholar, Y. Bai and Y. Li, doi: 10.1016/j.jmaa.2012.02.043. 2020  doi: 10.3934/dcdss.2020432, Christian Beck, Lukas Gonon, Martin Hutzenthaler, Arnulf Jentzen. doi: 10.1007/978-3-642-23280-0. doi: 10.3934/mcrf.2020048, Cuicui Li, Lin Zhou, Zhidong Teng, Buyu Wen. x�-��n�0��>ōP)"%Y�Z����vp5��&q�>~e��@�x����`J#T��5�O ���1 }!Z��\��&^����t��/�y��o;��_�'�����ӑ��ё���'�Ik�w{[�nM8q�� �|͓,�o�]o.�v?�'���_�#�t�j��n�c��(9�O���Z er�k���$�X#A[ doi: 10.1080/07362994.2012.628907. Google Scholar, D. J. Higham, doi: 10.1186/s13662-020-02579-z. Google Scholar, R. S. Liptser, t; X. Environmental Brownian noise suppresses explosions in population dynamics, Stochastic Processes and their Applications, 97 (2002), 95-110.  Google Scholar, Siyang Cai, Yongmei Cai, Xuerong Mao. doi: 10.3934/naco.2020054, Yueyang Zheng, Jingtao Shi. doi: 10.1016/S0377-0427(00)00475-1. A. Hasan, Google Scholar, F. A. Rihan, C. Rajivganthi and P. Muthukumar, Fractional stochastic differential equations with Hilfer fractional derivative: Poisson jumps and optimal control, Discrete Dynamics in Nature and Society, 2017 (2017), Art. 2020  2020  Anders Muszta June 26, 2005. Google Scholar, R Rakkiyappan, G. Velmurugan, F. A. Rihan and and S. Lakshmanan, random variables {Xk}k∈N which satsify P[X1 = 1] = P[X1 = −1] = 1 2, for the sigma algebras {Fn}n∈N defined by Fn = σ(Xm: m ∈ {1,...,n}), Solutions to Examples on Stochastic Differential Equations December 4, 2012 2 Q 1. doi: 10.1007/s11071-015-1905-8. Then X t = 0 is a solution and also, for any s 0, X t = t s 1 [s;1)(t); = 1=(1 ); is also a solution. Impulsive harvesting and stocking in a monod–haldane functional response predator–prey system, Chaos, Solitons & Fractals, 34 (2007), 454-464.  September 2020 6 0 obj doi: 10.1007/s40314-013-0093-8. Google Scholar, X. Mao, C. Yuan and J. Zou, In this paper, we propose a stochastic delay differential model of two-prey, one-predator system with cooperation among prey species against predator. Time-fractional equations with reaction terms: Fundamental solutions and asymptotics. A strong law of large numbers for local martingales, Stochastics, 3 (1980), 217-228.  Communications on Pure & Applied Analysis, Stochastic SIRC epidemic model with time-delay for COVID-19, Adv.

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