[1] Song X, Chen L. Persistence and global stability for nonautonomous predator-prey system with diffusion and time delay. Comput Math Appl, 1998, 35:33-40 [2] Cui J. The effect of dispersal on permanence in a Predator-Prey population growth model. Comput Math Appl, 2002, 44:1085-1097 [3] Chen F, Xie X. Permanence and extinction in nonlinear single and multiple species system with diffusion. Appl Math Comput, 2006, 177:410-426 [4] Song X, Chen L. Persistence and periodic orbits for two-species predator-prey system with diffusion. Canadian Appl Math Quart, 1998, 6:233-244 [5] Wei F, Lin Y, Que L, et al. Periodic solution and global stability for a nonautonomous competitive LotkaVolterra diffusion system. Appl Math Comput, 2010, 216:3097-3104 [6] Muhammadhaji A, Teng Z, Zhang L. Permanence in general nonautonomous predator-prey Lotka-Volterra systems with distributed delays and impulses. J Biol Syst, 2013, 21:1350012 [7] Muhammadhaji A, Teng Z, Rehim M. Dynamical behavior for a class of delayed Competitive-Mutulism systems. Differ Equ Dyn Syst, 2015, 23:281-301 [8] Xu R, Chaplain M, Davidson F A. Periodic solution of a Lotka-Volterra predator-prey model with dispersion and time delays. Appl Math Comput, 2004, 148:537-560 [9] Zhou X, Shi X, Song X. Analysis of nonautonomous predator-prey model with nonlinear diffusion and time delay. Appl Math Comput, 2008, 196:129-136 [10] Zhang Z, Wang Z. Periodic solutions of a two-species ratio-dependent predator-prey system with time delay in a two-patch environment. ANZIAM J, 2003, 45:233-244 [11] Liang R, Shen J. Positive periodic solutions for impulsive predator-prey model with dispersion and time delays. Appl Math Comput, 2010, 217:661-676 [12] Muhammadhaji A, Mahemuti R, Teng Z. On a periodic predator-prey system with nonlinear diffusion and delays. Afrika Matematika, 2016, 27:1179-1197 [13] Gopalsamy K, Weng P. Global attractivity in a competition system with feedback controls. Comput Math Appl, 2003, 45:665-676 [14] Chen F. The permanence and global attractivity of Lotka-Volterra competition system with feedback controls. Nonli Anal:RWA, 2006, 7:133-143 [15] Nie L, Tenga Z, Hu L, et al. Permanence and stability in nonautonomous predator-prey Lotka-Volterra systems with feedback controls. Computers and Mathematics with Applications, 2009, 58:436-448 [16] Chen F, Gong X, Pu L, et al. Dynamic behaviors of a Lotka-Volterra predator-prey system with feedback controls. J Biomathematics, 2015, 30:328-332(in Chinese) [17] Ding X, Wang F. Positive periodic solution for a semi-ratio-dependent predator-prey system with diffusion and time delays. Nonli Anal:RWA, 2008, 9:39-249 [18] Gopalsamy K, Weng P. Feedback regulation of logistic growth. Int J Math Math Sci, 1993, 16:177-192 [19] Xu J, Chen F. Permanence of a Lotka-Volterra cooperative system with time delays and feedback controls. Commun Math Biol Neurosci, 2015 [20] Xie W, Weng P. Existence of periodic solution for a predator-prey model with patch-diffusion and feedback control. Journal of South China Normal University (Natural Science Edition), 2012, 44:42-47(in Chinese) [21] Spagnolo B, Fiasconaro A, Valenti D. Noise induced phenomena in Lotka-Volterra systems. Fluctuation and Noise Letters, 2003, 3:L177-L185 [22] Spagnolo B, Cirone M, La Barbera A, et al. Noise-induced effects in population dynamics. J Phys:Condens Matter, 2002, 14:2247-2255 [23] Spagnolo B, Valenti D, Fiasconaro A. Noise in ecosystems:A short review. Math Biosci Engi, 2004, 1:185-211 [24] Lande R, Engen S, Saether B E. Stochastic Population Dynamics in Ecology and Conservation. Oxford:Oxford University Press, 2003 [25] Ridolfi L, Dodorico P, Laio F. Noise-Induced Phenomena in the Environmental Sciences. Cambridge:Cambridge University Press, 2011 [26] Liu Y, Shan M, Lian X. Stochastic extinction and persistence of a parasite-host epidemiological model. Physica A, 2016, 462:586-602 [27] Fiasconaro A, Spagnolo B. Resonant activation in piecewise linear asymmetric potentials. Phys Rev E, 2011, 83:041122 [28] Pizzolato N, Fiasconaro A, Persano Adorno D, et al. Resonant activation in polymer translocation:new insights into the escape dynamics of molecules driven by an oscillating field. Phys Biol, 2010, 7:034001 [29] Fiasconaro A, Mazo J J, Spagnolo B. Noise-induced enhancement of stability in a metastable system with damping. Phys Rev E, 2010, 82:041120 [30] Ciuchi S, de Pasquale, Spagnolo B. Nonlinear relaxation in the presence of an absorbing barrier. Phys Rev E, 1993, 47:3915-3926 [31] Bashkirtseva I, Ryashko L. How environmental noise can contract and destroy a persistence zone in population models with Allee effect. Theoretical Population Biology, 2017, 115:61-68 [32] Dubkov A, Spagnolo B. Langevin approach to Lévy flights in fixed potentials:Exact results for stationary probability distributions. Acta Phys Pol B, 2007, 38:1745-1758 [33] La Barberaa A, Spagnolo B. Spatio-temporal patterns in population dynamics. Physica A, 2002, 314:120-124 [34] Valenti D, Fiasconaro A, Spagnolo B. Pattern formation and spatial correlation induced by the noise in two competing species. Acta Physica Pol B, 2004, 35:1481-1489 [35] Mantegna R N, Spagnolo B, Testa L. Stochastic resonance in magnetic systems described by Preisach hysteresis model. J Appl Phys, 2005, 97:10E519/2 [36] Bashkirtseva I, Ryashko L. Noise-induced shifts in the population model with a weak Allee effect. Phys A, 2018, 491:28-36 [37] Sun G Q, Jin Z, Li L, Liu Q X. The role of noise in a predator-prey model with Allee effect. J Biol Phys, 2009, 35:185-196 [38] Gao J B, Hwang S K, Liu J M. When can noise induce chaos? Phys Rev Lett, 1999, 82:1132-1135 [39] Lai Y C, Tel T. Transient Chaos:Complex Dynamics on Finite Time Scales. Berlin:Springer, 2011 [40] Augello G, Valenti D, Spagnolo B. Non-Gaussian noise effects in the dynamics of a short overdamped Josephson junction. Eurn Phys J B, 2010, 78:225-234 [41] Shi Q H, Peng C M. Wellposedness for semirelativistic Schrodinger equation with power-type nonlinearity. Nonl Anal:TMA, 2019, 178:133-144 [42] Shi Q H, Wang S. Nonrelativistic approximation in the energy space for KGS system. J Math Anal Appl, 2018, 462:1242-1253 [43] Wang C Y, Zhou Y Q, Li Y H, Li R. Well-posedness of a ratio-dependent Lotka-Volterra system with feedback control. Boundary Value Problems, 2018, 2018:ID 117 [44] Wang C Y, Li L R, Zhou Y Q, Li R. On a delay ratio-dependent predator-prey system with feedback controls and shelter for the prey. Int J Biomath, 2018, 11(7):ID 1850095 [45] Boukhatem Y, Benabderrahmane B. General decay for a viscoelastic equation of variable coefficients with a time-varying delay in the boundary feedback and acoustic boundary conditions. Acta Math Sci, 2017, 37B(5):1453-1471 [46] Jia X J, Jia R A. Improve efficiency of biogas feedback supply chain in rural China. Acta Math Sci, 2017, 37B(3):768-785 [47] Apalara T A. Uniform decay in weakly dissipative timoshenko system with internal distributed delay feedbacks. Acta Math Sci, 2016, 36B(3):815-830 [48] Wang C Y, Liu H, Pan S, Su X L, Li R. Globally Attractive of a ratio-dependent Lotka-Volterra predatorprey model with feedback control. Adv Biosci Bioeng, 2016, 4(5):59-66 [49] Li N, Wang C Y. New existence results of positive solution for a class of nonlinear fractional differential equations. Acta Math Sci, 2013, 33B(3):847-854 [50] Yang X S, Cao J D. Adaptive pinning synchronization of coupled neural networks with mixed delays and vector-form stochastic perturbations. Acta Math Sci, 2012, 32B(3):955-977 [51] Chen F. On a nonlinear nonautonomous predator-prey model with diffusion and distributed delay. J Comput Appl Math, 2005, 180:33-49 [52] Nakata Y, Muroya Y. Permanence for nonautonomous Lotka-Volterra cooperative systems with delays. Nonli Anal:RWA, 2010, 11:528-534 [53] Khalil H K. Nonlinear Systems. 3rd ed. Englewood Cliffs:Prentice-Hall, 2002 [54] Basener W. Topology and its Applications. Hoboken:John Wiley and Sons, 2006 |