{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,12]],"date-time":"2025-10-12T03:50:41Z","timestamp":1760241041285,"version":"build-2065373602"},"reference-count":43,"publisher":"MDPI AG","issue":"4","license":[{"start":{"date-parts":[[2019,11,15]],"date-time":"2019-11-15T00:00:00Z","timestamp":1573776000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Axioms"],"abstract":"<jats:p>In biology, difference equations is often used to understand and describe life phenomenon through mathematical models. So, in this work, we study a new class of difference equations by focusing on the periodicity character, stability (local and global) and boundedness of its solutions. Furthermore, this equation involves a May\u2019s Host Parasitoid Model, as a special case.<\/jats:p>","DOI":"10.3390\/axioms8040131","type":"journal-article","created":{"date-parts":[[2019,11,15]],"date-time":"2019-11-15T11:25:56Z","timestamp":1573817156000},"page":"131","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":6,"title":["Global Analysis and the Periodic Character of a Class of Difference Equations"],"prefix":"10.3390","volume":"8","author":[{"given":"George E.","family":"Chatzarakis","sequence":"first","affiliation":[{"name":"Department of Electrical and Electronic Engineering Educators, School of Pedagogical and Technological Education (ASPETE), 14121 N. 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Mathematical Models in Biology: An Introduction, Cambridge University Press.","DOI":"10.1017\/CBO9780511790911"},{"key":"ref_6","doi-asserted-by":"crossref","unstructured":"Andres, J., and Pennequin, D. (2019). Note on Limit-Periodic Solutions of the Difference Equation xt+1 \u2212 [h(xt) + \u03bb]x = rt,\u03bb > 1. Axioms, 8.","DOI":"10.3390\/axioms8010019"},{"key":"ref_7","first-page":"89","article-title":"Stability analysis of a discrete ecological model","volume":"4","author":"Din","year":"2014","journal-title":"Comput. Ecol. Soft."},{"key":"ref_8","doi-asserted-by":"crossref","unstructured":"Grove, E.A., and Ladas, G. (2005). Periodicities in Nonlinear Difference Equations, Chapman & Hall\/CRC.","DOI":"10.1201\/9781420037722"},{"key":"ref_9","first-page":"85","article-title":"On the difference equation Jn+1 = (aJn\u2212l + bJn\u2212k)\/(cJn\u2212l + dJn\u2212k)","volume":"33","author":"Elabbasy","year":"2008","journal-title":"Acta Math. Vietnam."},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"187","DOI":"10.1007\/s11401-007-0456-9","article-title":"Dynamics of a rational difference equation","volume":"30","author":"Elabbasy","year":"2009","journal-title":"Chin. Ann. Math. Ser. B"},{"key":"ref_11","first-page":"082579","article-title":"On the difference equation Jn+1 = aJn\u2212l + bJn\u2212k + cJn\u2212s\/(dJn\u2212s \u2212 e)","volume":"1","year":"2016","journal-title":"Math. Methods Appl. Sci."},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"405628","DOI":"10.1155\/2013\/405628","article-title":"On a system of difference equations of an economic model","volume":"2013","author":"Elettreby","year":"2013","journal-title":"Discret. Dyn. Nat. Soc."},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"1463","DOI":"10.22436\/jnsa.009.04.06","article-title":"Dynamics and behavior of a higher order rational difference equation","volume":"9","author":"Elsayed","year":"2015","journal-title":"J. Nonlinear Sci. Appl."},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"241","DOI":"10.1007\/s11071-014-1660-2","article-title":"New method to obtain periodic solutions of period two and three of a rational difference equation","volume":"79","author":"Elsayed","year":"2015","journal-title":"Nonlinear Dyn."},{"key":"ref_15","first-page":"608","article-title":"On a max-type and a min-type difference equation","volume":"215","author":"Elsayed","year":"2009","journal-title":"Appl. Math. Comput."},{"key":"ref_16","first-page":"2012","article-title":"Dynamics and behavior of a higher order rational recursive sequence","volume":"69","author":"Elsayed","year":"2012","journal-title":"Adv. Differ. Equ."},{"key":"ref_17","doi-asserted-by":"crossref","unstructured":"Foupouagnigni, M., and Mboutngam, S. (2019). On the Polynomial Solution of Divided-Difference Equations of the Hypergeometric Type on Nonuniform Lattices. Axioms, 8.","DOI":"10.3390\/axioms8020047"},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"404","DOI":"10.3390\/axioms2030404","article-title":"On Solutions of Holonomic Divided-Difference Equations on Nonuniform Lattices","volume":"2","author":"Foupouagnigni","year":"2013","journal-title":"Axioms"},{"key":"ref_19","doi-asserted-by":"crossref","unstructured":"Gil, M. (2019). Solution Estimates for the Discrete Lyapunov Equation in a Hilbert Space and Applications to Difference Equations. Axioms, 8.","DOI":"10.3390\/axioms8010020"},{"key":"ref_20","doi-asserted-by":"crossref","unstructured":"Haghighi, A.M., and Mishev, D.P. (2013). Difference and Differential Equations with Applications in Queueing Theory, John Wiley & Sons Inc.","DOI":"10.1002\/9781118400678"},{"key":"ref_21","first-page":"701","article-title":"On the recursive sequnence Jn+1 = (\u03b1Jn\u22121 + \u03b2Jn\u22122)\/(\u03b3Jn\u22121 + \u03b4Jn\u22122)","volume":"9","author":"Kalabusic","year":"2003","journal-title":"J. Differ. Equ. Appl."},{"key":"ref_22","unstructured":"Kelley, W.G., and Peterson, A.C. (2001). Difference Equations: An Introduction with Applications, Harcour Academic. [2nd ed.]."},{"key":"ref_23","doi-asserted-by":"crossref","unstructured":"Kocic, V.L., and Ladas, G. (1993). Global Behavior of Nonlinear Difference Equations of Higher Order with Applications, Kluwer Academic Publishers.","DOI":"10.1007\/978-94-017-1703-8"},{"key":"ref_24","doi-asserted-by":"crossref","unstructured":"Kulenovic, M.R.S., and Ladas, G. (2001). Dynamics of Second Order Rational Difference Equations with Open Problems and Conjectures, Chapman & Hall\/CRC Press.","DOI":"10.1201\/9781420035384"},{"key":"ref_25","doi-asserted-by":"crossref","first-page":"2477","DOI":"10.1016\/j.apm.2009.11.012","article-title":"A note on the existence of periodic solutions in discrete predator-prey models","volume":"34","author":"Liu","year":"2010","journal-title":"Appl. Math. Model."},{"key":"ref_26","doi-asserted-by":"crossref","first-page":"2048941","DOI":"10.1155\/2019\/2048941","article-title":"Global behavior of a new rational nonlinear higher-order difference equation","volume":"2019","author":"Ma","year":"2019","journal-title":"Complexity"},{"key":"ref_27","doi-asserted-by":"crossref","unstructured":"Migda, M., and Migda, J. (2018). Nonoscillatory Solutions to Second-Order Neutral Difference Equations. Symmetry, 10.","DOI":"10.1155\/2018\/2368694"},{"key":"ref_28","doi-asserted-by":"crossref","first-page":"1043","DOI":"10.1007\/s11071-016-3293-0","article-title":"Comment on new method to obtain periodic solutions of period two and three of a rational difference equation [Nonlinear Dyn 79: 241\u2013250]","volume":"88","author":"Moaaz","year":"2017","journal-title":"Nonlinear Dyn."},{"key":"ref_29","first-page":"2018","article-title":"Dynamics of difference equation Jn+1 = f(Jn\u2212l, Jn\u2212k)","volume":"447","author":"Moaaz","year":"2018","journal-title":"Adv. Differ. Equ."},{"key":"ref_30","doi-asserted-by":"crossref","unstructured":"Moaaz, O., Chalishajar, D., and Bazighifan, O. (2019). Some Qualitative Behavior of Solutions of General Class of Difference Equations. Mathematics, 7.","DOI":"10.3390\/math7070585"},{"key":"ref_31","doi-asserted-by":"crossref","unstructured":"Pogrebkov, A. (2019). Hirota Difference Equation and Darboux System: Mutual Symmetry. Symmetry, 11.","DOI":"10.3390\/sym11030436"},{"key":"ref_32","first-page":"229","article-title":"On the recursive sequance xn+1 = \u03b1 + xn\u22121p\/xnp","volume":"18","author":"Stevic","year":"2005","journal-title":"J. Appl. Math. Comput."},{"key":"ref_33","doi-asserted-by":"crossref","first-page":"495","DOI":"10.1080\/10236190500539543","article-title":"A note on positive nonoscillatory solutions of the differential equation xn+1 = \u03b1 + xn\u22121p\/xnp","volume":"12","author":"Stevic","year":"2006","journal-title":"J. Diff. Eqs. Appl."},{"key":"ref_34","first-page":"911","article-title":"On the recursive sequence xn+1 = \u03b1n + xn\u22121\/xn","volume":"10","author":"Stevic","year":"2003","journal-title":"Dynam. Contin. Discret. Impuls. Syst. Ser. A Math. Anal."},{"key":"ref_35","doi-asserted-by":"crossref","first-page":"929","DOI":"10.1080\/10236190412331272616","article-title":"A note on periodic character of a difference equation","volume":"10","author":"Stevic","year":"2004","journal-title":"J. Differ. Equ. Appl."},{"key":"ref_36","doi-asserted-by":"crossref","first-page":"37264","DOI":"10.1155\/DDNS\/2006\/37264","article-title":"A short proof of the Cushing\u2013Henson conjecture","volume":"4","author":"Stevic","year":"2006","journal-title":"Discret. Dyn. Nat. Soc."},{"key":"ref_37","doi-asserted-by":"crossref","first-page":"60","DOI":"10.1016\/j.jmaa.2005.04.077","article-title":"Global stability and asymptotics of some classes of rational difference equations","volume":"316","author":"Stevic","year":"2006","journal-title":"J. Math. Anal. Appl."},{"key":"ref_38","first-page":"56813","article-title":"Asymptotics of some classes of higher order difference equations","volume":"2007","author":"Stevic","year":"2007","journal-title":"Discret. Dyn. Nat. Soc."},{"key":"ref_39","first-page":"13737","article-title":"Asymptotic periodicity of a higher order difference equation","volume":"2007","author":"Stevic","year":"2007","journal-title":"Discret. Dyn. Nat. Soc."},{"key":"ref_40","doi-asserted-by":"crossref","first-page":"28","DOI":"10.1016\/j.aml.2006.03.002","article-title":"Existence of nontrivial solutions of a rational difference equation","volume":"20","author":"Stevic","year":"2007","journal-title":"Appl. Math. Lett."},{"key":"ref_41","doi-asserted-by":"crossref","first-page":"195","DOI":"10.1016\/j.nahs.2019.02.006","article-title":"Stability analysis of a class of switched nonlinear systems using the time scale theory","volume":"33","author":"Taousser","year":"2019","journal-title":"Nonlinear Anal. 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