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Journal of Difference Equations and Applications Volume 19, 2013 - Issue 12
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Article

Local stability implies global stability for the 2-dimensional Ricker map

Ferenc A. BarthaCAPA Group, Department of Mathematics, University of Bergen, Bergen, Norway;Bolyai Institute, University of Szeged, Szeged, Hungary
,
Ábel GarabBolyai Institute, University of Szeged, Szeged, Hungary
&
Tibor KrisztinBolyai Institute, University of Szeged, Szeged, Hungary;Analysis and Stochastics Research Group, Bolyai Institute, Hungarian Academy of Sciences, University of Szeged, Szeged, HungaryCorrespondence[email protected]
Pages 2043-2078 | Received 13 Sep 2012, Accepted 07 May 2013, Published online: 01 Oct 2013

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Mats Gyllenberg, Jifa Jiang, Lei Niu & Ping Yan. (2019) On the dynamics of multi-species Ricker models admitting a carrying simplex. Journal of Difference Equations and Applications 25:11, pages 1489-1530.
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János Dudás. (2019) Global stability for the 2-dimensional logistic map. Journal of Difference Equations and Applications 25:2, pages 179-201.
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Robert J. Sacker & George R. Sell. (2017) Almost periodicity, Ricker map, Beverton-Holt map and others, a general method. Journal of Difference Equations and Applications 23:7, pages 1286-1297.
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Chunqing Wu & Patricia J. Y. Wong. (2016) Global asymptotical stability of the positive equilibrium of a logistic competitive model. Journal of Difference Equations and Applications 22:8, pages 1137-1155.
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Guo Lin & Ting Su. (2016) Asymptotic speeds of spread and traveling wave solutions of a second order integrodifference equation without monotonicity. Journal of Difference Equations and Applications 22:4, pages 554-569.
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Brian Ryals & Robert J. Sacker. (2015) Global stability in the 2D Ricker equation. Journal of Difference Equations and Applications 21:11, pages 1068-1081.
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Articles from other publishers (16)

Ferenc A. Bartha, Ferenc Bencs, Károly J. Böröczky & Daniel Hug. (2022) Extremizers and Stability of the Betke–Weil Inequality. Michigan Mathematical Journal -1:-1.
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János Dudás & Tibor Krisztin. (2021) Global stability for the three-dimensional logistic map. Nonlinearity 34:2, pages 894-938.
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Robert Szczelina & Piotr Zgliczyński. (2017) Algorithm for Rigorous Integration of Delay Differential Equations and the Computer-Assisted Proof of Periodic Orbits in the Mackey–Glass Equation. Foundations of Computational Mathematics 18:6, pages 1299-1332.
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Irina Bashkirtseva & Lev Ryashko. (2018) Stochastic Sensitivity Analysis of Noise-Induced Extinction in the Ricker Model with Delay and Allee Effect. Bulletin of Mathematical Biology 80:6, pages 1596-1614.
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Ábel Garab. (2018) A note on dissipativity and permanence of delay difference equations. Electronic Journal of Qualitative Theory of Differential Equations:51, pages 1-12.
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Daniel Franco, Juan Perán & Juan Segura. (2018) Global stability of discrete dynamical systems via exponent analysis: applications to harvesting population models. Electronic Journal of Qualitative Theory of Differential Equations:101, pages 1-22.
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Irina Bashkirtseva. (2017) Preventing Noise-Induced Extinction in Discrete Population Models. Discrete Dynamics in Nature and Society 2017, pages 1-10.
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Elena Braverman, George E Chatzarakis & Ioannis P Stavroulakis. (2016) Iterative oscillation tests for differential equations with several non-monotone arguments. Advances in Difference Equations 2016:1.
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Víctor Jiménez López & Enrique Parreño. (2016) L.A.S. and Negative Schwarzian Derivative Do Not Imply G.A.S. in Clark’s Equation. Journal of Dynamics and Differential Equations 28:2, pages 339-374.
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J. Perán & D. Franco. (2015) Global convergence of the second order Ricker equation. Applied Mathematics Letters 47, pages 47-53.
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Ferenc A. Bartha & Warwick Tucker. (2015) Fixed points of a destabilized Kuramoto–Sivashinsky equation. Applied Mathematics and Computation 266, pages 339-349.
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Elena Braverman & Daniel Franco. (2015) Stabilization with target oriented control for higher order difference equations. Physics Letters A 379:16-17, pages 1102-1109.
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Nicolas Delanoue, Luc Jaulin & Bertrand Cottenceau. (2015) An algorithm for computing a neighborhood included in the attraction domain of an asymptotically stable point. Communications in Nonlinear Science and Numerical Simulation 21:1-3, pages 181-189.
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Irina Bashkirtseva & Lev Ryashko. (2014) Stochastic sensitivity analysis of the attractors for the randomly forced Ricker model with delay. Physics Letters A 378:48, pages 3600-3606.
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Ferenc A. Bartha & Ábel Garab. (2014) Necessary and sufficient condition for the global stability of a delayed discrete-time single neuron model. Journal of Computational Dynamics 1:2, pages 213-232.
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Balázs Bánhelyi, Tibor Csendes, Tibor Krisztin & Arnold Neumaier. (2014) Global Attractivity of the Zero Solution for Wright's Equation. SIAM Journal on Applied Dynamical Systems 13:1, pages 537-563.
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