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dc.contributor.authorHuang, Chun-Mingen_US
dc.contributor.authorJuang, Jonqen_US
dc.date.accessioned2016-03-28T00:04:11Z-
dc.date.available2016-03-28T00:04:11Z-
dc.date.issued2015-11-01en_US
dc.identifier.issn0218-1274en_US
dc.identifier.urihttp://dx.doi.org/10.1142/S0218127415501576en_US
dc.identifier.urihttp://hdl.handle.net/11536/129391-
dc.description.abstractIn previous papers [Isagi et al., 1997; Satake & Iwasa, 2000], a forest model was proposed. The authors demonstrated numerically that the mature forest could possibly exhibit annual reproduction (fixed point synchronization), periodic and chaotic synchronization as the energy depletion constant d is gradually increased. To understand such rich synchronization phenomena, we are led to study global dynamics of a piecewise smooth map f(d,beta) containing two parameters d and beta. Here d is the energy depletion quantity and beta is the coupling strength. In particular, we obtain the following results. First, we prove that f(d,0) has a chaotic dynamic in the sense of Devaney on an invariant set whenever d > 1, which improves a result of [Chang & Chen, 2011]. Second, we prove, via the Schwarzian derivative and a generalized result of [Singer, 1978], that f(d,beta) exhibits the period adding bifurcation. Specifically, we show that for any beta > 0, f(d,beta) has a unique global attracting fixed point whenever d <= 1/(beta+ 1)(beta+ 1/beta+ 2)beta (< 1) and that for any beta > 0, f(d,beta) has a unique attracting period k + 1 point whenever d is less than and near any positive integer k. Furthermore, the corresponding period k + 1 point instantly becomes unstable as d moves pass the integer k. Finally, we demonstrate numerically that there are chaotic dynamics whenever d is in between and away from two consecutive positive integers. We also observe the route to chaos as d increases from one positive integer to the next through finite period doubling.en_US
dc.language.isoen_USen_US
dc.subjectCoupled map latticesen_US
dc.subjectglobal synchronizationen_US
dc.subjectSchwarzian derivativeen_US
dc.titleBifurcation and Chaos in Synchronous Manifold of a Forest Modelen_US
dc.typeArticleen_US
dc.identifier.doi10.1142/S0218127415501576en_US
dc.identifier.journalINTERNATIONAL JOURNAL OF BIFURCATION AND CHAOSen_US
dc.citation.volume25en_US
dc.citation.issue12en_US
dc.contributor.department應用數學系zh_TW
dc.contributor.department數學建模與科學計算所(含中心)zh_TW
dc.contributor.departmentDepartment of Applied Mathematicsen_US
dc.contributor.departmentGraduate Program of Mathematical Modeling and Scientific Computing, Department of Applied Mathematicsen_US
dc.identifier.wosnumberWOS:000366301200005en_US
dc.citation.woscount0en_US
Appears in Collections:Articles