{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,7,8]],"date-time":"2026-07-08T00:18:08Z","timestamp":1783469888222,"version":"3.55.0"},"reference-count":60,"publisher":"Elsevier BV","license":[{"start":{"date-parts":[[2026,11,1]],"date-time":"2026-11-01T00:00:00Z","timestamp":1793491200000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.elsevier.com\/tdm\/userlicense\/1.0\/"},{"start":{"date-parts":[[2026,11,1]],"date-time":"2026-11-01T00:00:00Z","timestamp":1793491200000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.elsevier.com\/legal\/tdmrep-license"}],"content-domain":{"domain":["elsevier.com","sciencedirect.com"],"crossmark-restriction":true},"short-container-title":["Mathematics and Computers in Simulation"],"published-print":{"date-parts":[[2026,11]]},"DOI":"10.1016\/j.matcom.2026.05.024","type":"journal-article","created":{"date-parts":[[2026,5,28]],"date-time":"2026-05-28T07:03:42Z","timestamp":1779951822000},"page":"633-667","update-policy":"https:\/\/doi.org\/10.1016\/elsevier_cm_policy","source":"Crossref","is-referenced-by-count":0,"special_numbering":"C","title":["Degenerate Hopf and homoclinic bifurcations in a prey\u2013predator model with Allee-inducing escape ability of prey"],"prefix":"10.1016","volume":"249","author":[{"ORCID":"https:\/\/orcid.org\/0009-0003-8145-2577","authenticated-orcid":false,"given":"Kavitha Shree","family":"Kumaresan","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0009-0008-9371-7612","authenticated-orcid":false,"given":"Shri Harine","family":"P","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-2540-4488","authenticated-orcid":false,"given":"Ankit","family":"Kumar","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"78","reference":[{"key":"10.1016\/j.matcom.2026.05.024_b1","doi-asserted-by":"crossref","first-page":"377","DOI":"10.1111\/1365-2435.12347","article-title":"Predator-free space, functional responses and biological invasions","volume":"29","author":"Barrios-O\u2019Neill","year":"2015","journal-title":"Funct. Ecol."},{"key":"10.1016\/j.matcom.2026.05.024_b2","series-title":"Ecology: From Individuals to Ecosystems","author":"Begon","year":"2020"},{"key":"10.1016\/j.matcom.2026.05.024_b3","doi-asserted-by":"crossref","first-page":"531","DOI":"10.1016\/j.anbehav.2009.12.014","article-title":"Spatial responses to predators vary with prey escape mode","volume":"79","author":"Wirsing","year":"2010","journal-title":"Anim. Behav."},{"key":"10.1016\/j.matcom.2026.05.024_b4","doi-asserted-by":"crossref","first-page":"141","DOI":"10.1146\/annurev.ps.36.020185.001041","article-title":"The ecology of foraging behavior: implications for animal learning and memory","volume":"36","author":"Kamil","year":"1985","journal-title":"Annu. Rev. Psychol."},{"key":"10.1016\/j.matcom.2026.05.024_b5","doi-asserted-by":"crossref","first-page":"577","DOI":"10.1016\/S0149-7634(01)00042-2","article-title":"Antipredator responses and defensive behavior: ecological and ethological approaches for the neurosciences","volume":"25","author":"Kavaliers","year":"2001","journal-title":"Neurosci. Biobehav. Rev."},{"key":"10.1016\/j.matcom.2026.05.024_b6","series-title":"Elements of Physical Biology","author":"Lotka","year":"1925"},{"key":"10.1016\/j.matcom.2026.05.024_b7","doi-asserted-by":"crossref","first-page":"777","DOI":"10.1007\/s11071-015-1905-8","article-title":"Fractional-order delayed predator\u2013prey systems with holling type-II functional response","volume":"80","author":"Rihan","year":"2015","journal-title":"Nonlinear Dynam."},{"key":"10.1016\/j.matcom.2026.05.024_b8","doi-asserted-by":"crossref","first-page":"54","DOI":"10.1016\/j.matcom.2025.11.016","article-title":"The impact of human shields in autonomous and non-autonomous prey-predator models with modified cosner functional response","volume":"242","author":"Roy","year":"2025","journal-title":"Math. Comput. Simulation"},{"key":"10.1016\/j.matcom.2026.05.024_b9","doi-asserted-by":"crossref","first-page":"219","DOI":"10.1007\/s40435-025-01718-2","article-title":"Stability and bifurcation analysis in a novel discrete prey-predator system incorporating moonlight, water availability, and vigilance effects","volume":"13","author":"Mokni","year":"2025","journal-title":"Int. J. Dyn. Control."},{"key":"10.1016\/j.matcom.2026.05.024_b10","first-page":"385","article-title":"Some characteristics of simple types of predation and parasitism1","volume":"91","author":"Holling","year":"1959","journal-title":"Can. \u00c8ntomol."},{"key":"10.1016\/j.matcom.2026.05.024_b11","doi-asserted-by":"crossref","first-page":"209","DOI":"10.1086\/282272","article-title":"Graphical representation and stability conditions of predator-prey interactions","volume":"97","author":"Rosenzweig","year":"1963","journal-title":"Amer. Nat."},{"key":"10.1016\/j.matcom.2026.05.024_b12","doi-asserted-by":"crossref","first-page":"11","DOI":"10.1016\/j.ecocom.2018.10.004","article-title":"Complexity in a prey-predator model with prey refuge and diffusion","volume":"37","author":"Chakraborty","year":"2019","journal-title":"Ecol. Complex."},{"key":"10.1016\/j.matcom.2026.05.024_b13","doi-asserted-by":"crossref","first-page":"528","DOI":"10.1016\/j.cnsns.2018.07.019","article-title":"Global stability and hopf-bifurcation of prey-predator system with two discrete delays including habitat complexity and prey refuge","volume":"67","author":"Dubey","year":"2019","journal-title":"Commun. Nonlinear Sci. Numer. Simul."},{"key":"10.1016\/j.matcom.2026.05.024_b14","series-title":"Escape behaviour: importance, scope, and variables","author":"Cooper","year":"2015"},{"key":"10.1016\/j.matcom.2026.05.024_b15","doi-asserted-by":"crossref","first-page":"24","DOI":"10.1016\/j.cobeha.2016.08.006","article-title":"Escape behavior: dynamic decisions and a growing consensus","volume":"12","author":"Blumstein","year":"2016","journal-title":"Curr. Opin. Behav. Sci."},{"key":"10.1016\/j.matcom.2026.05.024_b16","doi-asserted-by":"crossref","first-page":"440","DOI":"10.1038\/s41467-017-00373-2","article-title":"Unpredictability of escape trajectory explains predator evasion ability and microhabitat preference of desert rodents","volume":"8","author":"Moore","year":"2017","journal-title":"Nat. Commun."},{"key":"10.1016\/j.matcom.2026.05.024_b17","doi-asserted-by":"crossref","first-page":"4328","DOI":"10.1242\/jeb.111773","article-title":"Prey fish escape by sensing the bow wave of a predator","volume":"217","author":"Stewart","year":"2014","journal-title":"J. Exp. Biol."},{"key":"10.1016\/j.matcom.2026.05.024_b18","doi-asserted-by":"crossref","DOI":"10.1016\/j.chaos.2022.112091","article-title":"Fear effect in a predator-prey model with additional food, prey refuge and harvesting on super predator","volume":"159","author":"Thirthar","year":"2022","journal-title":"Chaos Solitons Fractals"},{"key":"10.1016\/j.matcom.2026.05.024_b19","doi-asserted-by":"crossref","first-page":"58","DOI":"10.1016\/j.chaos.2014.11.008","article-title":"Bifurcation analysis of a predator\u2013prey model with anti-predator behaviour","volume":"70","author":"Tang","year":"2015","journal-title":"Chaos Solitons Fractals"},{"key":"10.1016\/j.matcom.2026.05.024_b20","doi-asserted-by":"crossref","first-page":"9819","DOI":"10.1002\/mma.10845","article-title":"Global dynamics of a stage structure prey\u2013predator model with fear, group defense, and antipredator behavior","volume":"48","author":"KP","year":"2025","journal-title":"Math. Methods Appl. Sci."},{"key":"10.1016\/j.matcom.2026.05.024_b21","doi-asserted-by":"crossref","first-page":"776","DOI":"10.1111\/j.0014-3820.2002.tb01388.x","article-title":"Rapid evolution of escape ability in trinidadian guppies (poecilia reticulata)","volume":"56","author":"O\u2019Steen","year":"2002","journal-title":"Evolution"},{"key":"10.1016\/j.matcom.2026.05.024_b22","doi-asserted-by":"crossref","first-page":"357","DOI":"10.1038\/346357a0","article-title":"Experimentally induced life-history evolution in a natural population","volume":"346","author":"Reznick","year":"1990","journal-title":"Nature"},{"key":"10.1016\/j.matcom.2026.05.024_b23","doi-asserted-by":"crossref","first-page":"3413","DOI":"10.1890\/07-1057.1","article-title":"Habitat complexity influences cascading effects of multiple predators","volume":"89","author":"Grabowski","year":"2008","journal-title":"Ecology"},{"key":"10.1016\/j.matcom.2026.05.024_b24","doi-asserted-by":"crossref","first-page":"2958","DOI":"10.1111\/1365-2656.13353","article-title":"Habitat features and performance interact to determine the outcomes of terrestrial predator\u2013prey pursuits","volume":"89","author":"Wheatley","year":"2020","journal-title":"J. Anim. Ecol."},{"key":"10.1016\/j.matcom.2026.05.024_b25","doi-asserted-by":"crossref","DOI":"10.1016\/j.jembe.2020.151333","article-title":"Effects of a habitat-modifying eelgrass epibiont on predator success and epifaunal survival","volume":"526","author":"Ledbetter","year":"2020","journal-title":"J. Exp. Mar. Biology Ecol."},{"key":"10.1016\/j.matcom.2026.05.024_b26","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1140\/epjp\/s13360-020-00897-5","article-title":"Self-diffusion-driven pattern formation in prey\u2013predator system with complex habitat under fear effect","volume":"135","author":"Jana","year":"2020","journal-title":"Eur. Phys. J. Plus"},{"key":"10.1016\/j.matcom.2026.05.024_b27","doi-asserted-by":"crossref","first-page":"431","DOI":"10.3390\/d14060431","article-title":"Habitat complexity alters predator-prey interactions in a shallow water ecosystem","volume":"14","author":"Froneman","year":"2022","journal-title":"Diversity"},{"key":"10.1016\/j.matcom.2026.05.024_b28","doi-asserted-by":"crossref","first-page":"810","DOI":"10.3934\/mbe.2025029","article-title":"Predator-prey dynamics with refuge, alternate food, and harvesting strategies in a patchy habitat","volume":"22","author":"Manoharan","year":"2025","journal-title":"Math. Biosci. Eng."},{"key":"10.1016\/j.matcom.2026.05.024_b29","doi-asserted-by":"crossref","DOI":"10.1142\/S0218127424500615","article-title":"Spatiotemporal and trade-off dynamics in prey\u2013predator model with domed functional response and fear effect","volume":"34","author":"Bhargava","year":"2024","journal-title":"Int. J. Bifurc. Chaos"},{"key":"10.1016\/j.matcom.2026.05.024_b30","doi-asserted-by":"crossref","first-page":"581","DOI":"10.1086\/512688","article-title":"Habitat choice in predator-prey systems: spatial instability due to interacting adaptive movements","volume":"169","author":"Abrams","year":"2007","journal-title":"Amer. Nat."},{"key":"10.1016\/j.matcom.2026.05.024_b31","doi-asserted-by":"crossref","DOI":"10.1002\/ecy.2724","article-title":"Habitat complexity mediates the predator\u2013prey space race","volume":"100","author":"Smith","year":"2019","journal-title":"Ecology"},{"key":"10.1016\/j.matcom.2026.05.024_b32","doi-asserted-by":"crossref","first-page":"131","DOI":"10.1006\/tpbi.1998.1351","article-title":"Effects of optimal antipredator behavior of prey on predator\u2013prey dynamics: the role of refuges","volume":"53","author":"K\u0159ivan","year":"1998","journal-title":"Theor. POpulation BIology"},{"key":"10.1016\/j.matcom.2026.05.024_b33","doi-asserted-by":"crossref","first-page":"431","DOI":"10.1086\/284719","article-title":"Antipredator behavior and the population dynamics of simple predator-prey systems","volume":"130","author":"Ives","year":"1987","journal-title":"Amer. Nat."},{"key":"10.1016\/j.matcom.2026.05.024_b34","doi-asserted-by":"crossref","first-page":"1802","DOI":"10.2307\/1940122","article-title":"Habitat structural complexity and the interaction between bluegills and their prey","volume":"63","author":"Crowder","year":"1982","journal-title":"Ecology"},{"key":"10.1016\/j.matcom.2026.05.024_b35","doi-asserted-by":"crossref","first-page":"158","DOI":"10.1007\/BF00380145","article-title":"Predator foraging success and habitat complexity: quantitative test of the threshold hypothesis","volume":"80","author":"Gotceitas","year":"1989","journal-title":"Oecologia"},{"key":"10.1016\/j.matcom.2026.05.024_b36","doi-asserted-by":"crossref","first-page":"300","DOI":"10.1007\/s00442-005-0198-x","article-title":"Habitat complexity and sex-dependent predation of mosquito larvae in containers","volume":"146","author":"Alto","year":"2005","journal-title":"Oecologia"},{"key":"10.1016\/j.matcom.2026.05.024_b37","doi-asserted-by":"crossref","first-page":"458","DOI":"10.1016\/j.jtbi.2010.07.008","article-title":"Density-dependent dispersal and relative dispersal affect the stability of predator\u2013prey metacommunities","volume":"266","author":"Hauzy","year":"2010","journal-title":"J. Theoret. Biol."},{"key":"10.1016\/j.matcom.2026.05.024_b38","doi-asserted-by":"crossref","DOI":"10.1016\/j.jmaa.2022.126174","article-title":"Density-dependent diffusion and refuge in a spatial rosenzweig-macarthur model: Stability results","volume":"512","author":"Rodriguez","year":"2022","journal-title":"J. Math. Anal. Appl."},{"key":"10.1016\/j.matcom.2026.05.024_b39","doi-asserted-by":"crossref","first-page":"14629","DOI":"10.3934\/math.2025659","article-title":"Complex dynamics of a discretized rosenzweig\u2013macarthur prey-predator model with fear effect on prey and prey refuge","volume":"10","author":"Uddin","year":"2025","journal-title":"AIMS Math."},{"key":"10.1016\/j.matcom.2026.05.024_b40","doi-asserted-by":"crossref","DOI":"10.1016\/j.cnsns.2023.107700","article-title":"Dynamical inquest of refuge and bubbling issues in an interacting species system","volume":"129","author":"Mandal","year":"2024","journal-title":"Commun. Nonlinear Sci. Numer. Simul."},{"key":"10.1016\/j.matcom.2026.05.024_b41","series-title":"Ordinary Differential Equations, Ginn and Co","author":"Birkhoff","year":"1982"},{"key":"10.1016\/j.matcom.2026.05.024_b42","volume":"vol. 7","author":"Perko","year":"2013"},{"key":"10.1016\/j.matcom.2026.05.024_b43","volume":"vol. 112","author":"Kuznetsov","year":"1998"},{"key":"10.1016\/j.matcom.2026.05.024_b44","doi-asserted-by":"crossref","first-page":"976","DOI":"10.1016\/j.matcom.2021.06.024","article-title":"Bifurcation analysis in a predator\u2013prey system with an increasing functional response and constant-yield prey harvesting","volume":"190","author":"Shang","year":"2021","journal-title":"Math. Comput. Simulation"},{"key":"10.1016\/j.matcom.2026.05.024_b45","doi-asserted-by":"crossref","first-page":"7483","DOI":"10.1007\/s11071-024-10706-8","article-title":"Global dynamics of an ecological model in presences of fear and group defense in prey and Allee effect in predator","volume":"113","author":"Kumar","year":"2025","journal-title":"Nonlinear Dynam."},{"key":"10.1016\/j.matcom.2026.05.024_b46","doi-asserted-by":"crossref","first-page":"481","DOI":"10.1137\/0148027","article-title":"Generalized hopf bifurcation and its dual generalized homoclinic bifurcation","volume":"48","author":"Joyal","year":"1988","journal-title":"SIAM J. Appl. Math."},{"key":"10.1016\/j.matcom.2026.05.024_b47","series-title":"Nonlinear Dynamics and Chaos: With Applications to Physics, Biology, Chemistry, and Engineering","author":"Strogatz","year":"2024"},{"key":"10.1016\/j.matcom.2026.05.024_b48","doi-asserted-by":"crossref","DOI":"10.1016\/j.jtbi.2020.110542","article-title":"Ecological and evolutionary consequences of predator-prey role reversal: Allee effect and catastrophic predator extinction","volume":"510","author":"Lehtinen","year":"2021","journal-title":"J. Theoret. Biol."},{"key":"10.1016\/j.matcom.2026.05.024_b49","doi-asserted-by":"crossref","first-page":"444","DOI":"10.1007\/s11538-009-9454-2","article-title":"Modelling disease introduction as biological control of invasive predators to preserve endangered prey","volume":"72","author":"Oliveira","year":"2010","journal-title":"Bull. Math. Biol."},{"key":"10.1016\/j.matcom.2026.05.024_b50","doi-asserted-by":"crossref","first-page":"13","DOI":"10.1016\/j.jtbi.2017.02.002","article-title":"Hunting cooperation and Allee effects in predators","volume":"419","author":"Alves","year":"2017","journal-title":"J. Theoret. Biol."},{"key":"10.1016\/j.matcom.2026.05.024_b51","article-title":"Local and global dynamics of a prey\u2013predator system with fear, allee effect, and variable attack rate","volume":"34","author":"Shri Harine","year":"2024","journal-title":"Chaos: Interdiscip. J. Nonlinear Sci."},{"key":"10.1016\/j.matcom.2026.05.024_b52","doi-asserted-by":"crossref","first-page":"1272","DOI":"10.1007\/s11538-008-9299-0","article-title":"Determining important parameters in the spread of malaria through the sensitivity analysis of a mathematical model","volume":"70","author":"Chitnis","year":"2008","journal-title":"Bull. Math. Biol."},{"key":"10.1016\/j.matcom.2026.05.024_b53","doi-asserted-by":"crossref","DOI":"10.1016\/j.chaos.2024.114949","article-title":"Allee-induced bubbling phenomena in an interacting species model","volume":"184","author":"Mandal","year":"2024","journal-title":"Chaos Solitons Fractals"},{"key":"10.1016\/j.matcom.2026.05.024_b54","doi-asserted-by":"crossref","first-page":"32","DOI":"10.1016\/j.matcom.2024.09.026","article-title":"Dynamics of a Leslie\u2013Gower type predator\u2013prey system with herd behavior and constant harvesting in prey","volume":"229","author":"Yao","year":"2025","journal-title":"Math. Comput. Simulation"},{"key":"10.1016\/j.matcom.2026.05.024_b55","doi-asserted-by":"crossref","first-page":"9","DOI":"10.1007\/s00265-006-0232-y","article-title":"The dynamic nature of antipredator behavior: prey fish integrate threat-sensitive antipredator responses within background levels of predation risk","volume":"61","author":"Brown","year":"2006","journal-title":"Behav. Ecol. Sociobiol."},{"key":"10.1016\/j.matcom.2026.05.024_b56","doi-asserted-by":"crossref","first-page":"556","DOI":"10.1111\/j.1365-2656.2008.01512.x","article-title":"Towards a predictive framework for predator risk effects: the interaction of landscape features and prey escape tactics","volume":"78","author":"Heithaus","year":"2009","journal-title":"J. Anim. Ecol."},{"key":"10.1016\/j.matcom.2026.05.024_b57","doi-asserted-by":"crossref","DOI":"10.1016\/j.ecocom.2020.100889","article-title":"Dynamics of a stochastic predator-prey model with habitat complexity and prey aggregation","volume":"45","author":"Zhang","year":"2021","journal-title":"Ecol. Complex."},{"key":"10.1016\/j.matcom.2026.05.024_b58","first-page":"40","article-title":"Degenerate homoclinic and hopf bifurcation in a stage-structured model with parental care in fearful prey and group defense","volume":"241","author":"Shri Harine","year":"2025","journal-title":"Math. Comput. Simulation"},{"key":"10.1016\/j.matcom.2026.05.024_b59","doi-asserted-by":"crossref","first-page":"387","DOI":"10.1007\/s00442-019-04425-w","article-title":"Time to revisit? a predator\u2019s previous successes and failures in prey capture determine its return time to patches","volume":"190","author":"Vijayan","year":"2019","journal-title":"Oecologia"},{"key":"10.1016\/j.matcom.2026.05.024_b60","doi-asserted-by":"crossref","first-page":"1052","DOI":"10.1086\/285372","article-title":"Prey uncertainty and the balancing of antipredator and feeding needs","volume":"139","author":"Sih","year":"1992","journal-title":"Amer. Nat."}],"container-title":["Mathematics and Computers in Simulation"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/api.elsevier.com\/content\/article\/PII:S0378475426002211?httpAccept=text\/xml","content-type":"text\/xml","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/api.elsevier.com\/content\/article\/PII:S0378475426002211?httpAccept=text\/plain","content-type":"text\/plain","content-version":"vor","intended-application":"text-mining"}],"deposited":{"date-parts":[[2026,7,7]],"date-time":"2026-07-07T23:54:09Z","timestamp":1783468449000},"score":1,"resource":{"primary":{"URL":"https:\/\/linkinghub.elsevier.com\/retrieve\/pii\/S0378475426002211"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2026,11]]},"references-count":60,"alternative-id":["S0378475426002211"],"URL":"https:\/\/doi.org\/10.1016\/j.matcom.2026.05.024","relation":{},"ISSN":["0378-4754"],"issn-type":[{"value":"0378-4754","type":"print"}],"subject":[],"published":{"date-parts":[[2026,11]]},"assertion":[{"value":"Elsevier","name":"publisher","label":"This article is maintained by"},{"value":"Degenerate Hopf and homoclinic bifurcations in a prey\u2013predator model with Allee-inducing escape ability of prey","name":"articletitle","label":"Article Title"},{"value":"Mathematics and Computers in Simulation","name":"journaltitle","label":"Journal Title"},{"value":"https:\/\/doi.org\/10.1016\/j.matcom.2026.05.024","name":"articlelink","label":"CrossRef DOI link to publisher maintained version"},{"value":"article","name":"content_type","label":"Content Type"},{"value":"\u00a9 2026 Published by Elsevier B.V. on behalf of International Association for Mathematics and Computers in Simulation (IMACS).","name":"copyright","label":"Copyright"}]}}