메뉴 건너뛰기




Volumn 20, Issue 2, 2010, Pages 197-211

The structure of infinite periodic and chaotic hub cascades in phase diagrams of simple autonomous flows

Author keywords

Chemical oscillators; Dense laser chaos; Global bifurcations; HindmarshRose neuronal chaos; Homoclinic orbits; Hubs and spirals; Phase diagrams; R ssler oscillators; T points

Indexed keywords

CONTINUOUS TIME SYSTEMS; CONTROL NONLINEARITIES; DIFFERENTIAL EQUATIONS; DYNAMICAL SYSTEMS; GRAPHIC METHODS; NEURAL NETWORKS; ORDINARY DIFFERENTIAL EQUATIONS; PHASE DIAGRAMS;

EID: 77951591069     PISSN: 02181274     EISSN: None     Source Type: Journal    
DOI: 10.1142/S0218127410025636     Document Type: Conference Paper
Times cited : (124)

References (52)
  • 1
    • 44749089228 scopus 로고    scopus 로고
    • Self-similar structures in a 2d parameter-space of an inductorless chua's circuit
    • Albuquerque, H. A., Rubinger, R. M. & Rech, P. C. [2008] "Self-similar structures in a 2D parameter-space of an inductorless Chua's circuit, " Phys. Lett. A 372, 4793-4798.
    • (2008) Phys. Lett. A , vol.372 , pp. 4793-4798
    • Albuquerque, H.A.1    Rubinger, R.M.2    Rech, P.C.3
  • 2
    • 0345779413 scopus 로고
    • Systematics of the lorenz model at σ = 10
    • Alfsen, K. H. & Frøyland, J. [1985] "Systematics of the Lorenz model at σ = 10, " Phys. Scripta 31, 15-20.
    • (1985) Phys. Scripta , vol.31 , pp. 15-20
    • Alfsen, K.H.1    Frøyland, J.2
  • 3
    • 35348914401 scopus 로고    scopus 로고
    • Critical behavior of the Lyapunov exponent in type-III intermittency
    • DOI 10.1016/j.chaos.2006.06.017, PII S0960077906005959
    • Alvarez-Llamoza, O., Cosenza, M. G. & Ponce, G. A. [2008] "Critical behavior of the Lyapunov exponent in type-III intermittency, " Chaos Solit. Fract. 36, 150-156. (Pubitemid 47576647)
    • (2008) Chaos, Solitons and Fractals , vol.36 , Issue.1 , pp. 150-156
    • Alvarez-Llamoza, O.1    Cosenza, M.G.2    Ponce, G.A.3
  • 4
    • 0035324743 scopus 로고    scopus 로고
    • Example of robust chaos in a smooth map
    • DOI 10.1209/epl/i2001-00241-3
    • Andrecut, M. & Ali, M. K. [2001] "Robust chaos in smooth unimodal maps, " Phys. Rev. E 64, 025203R. (Pubitemid 33271105)
    • (2001) Europhysics Letters , vol.54 , Issue.3 , pp. 300-305
    • Andrecut, M.1    Ali, M.K.2
  • 8
    • 49149128642 scopus 로고    scopus 로고
    • Periodicity hub and nested spirals in the phase diagram of a simple resistive circuit
    • Bonatto, C. & Gallas, J. A. C. [2008a] "Periodicity hub and nested spirals in the phase diagram of a simple resistive circuit, " Phys. Rev. Lett. 101, 054101.
    • (2008) Phys. Rev. Lett. , vol.101 , pp. 054101
    • Bonatto, C.1    Gallas, J.A.C.2
  • 9
    • 38349014314 scopus 로고    scopus 로고
    • Accumulation boundaries: Codimension-two accumulation of accumulations in phase diagrams of semiconductor lasers, electric circuits, atmospheric, and chemical oscillators
    • Bonatto, C. & Gallas, J. A. C. [2008b] "Accumulation boundaries: Codimension-two accumulation of accumulations in phase diagrams of semiconductor lasers, electric circuits, atmospheric, and chemical oscillators, " Phil. Trans. Royal Soc. London, Series A 366, 505-517.
    • (2008) Phil. Trans. Royal Soc. London, Series A , vol.366 , pp. 505-517
    • Bonatto, C.1    Gallas, J.A.C.2
  • 12
    • 0000595586 scopus 로고
    • The bifuraction of separatrix contours and chaos
    • Bykov, V. V. [1993] "The bifuraction of separatrix contours and chaos, " Physica D 62, 290-299.
    • (1993) Physica D , vol.62 , pp. 290-299
    • Bykov, V.V.1
  • 14
    • 0043018355 scopus 로고    scopus 로고
    • Synchronization and collective behavior in globally coupled logarithmic maps
    • Cosenza, M. G. & González, J. [1998] "Synchronization and collective behavior in globally coupled logarithmic maps, " Prog. Theor. Phys. 100, 21-38. (Pubitemid 128139415)
    • (1998) Progress of Theoretical Physics , vol.100 , Issue.1 , pp. 21-38
    • Cosenza, M.G.1    Gonzalez, J.2
  • 15
    • 44149085182 scopus 로고    scopus 로고
    • On the robustness of chaos in dynamical systems: Theories and applications
    • Elhadj, Z. & Sprott, J. C. [2008] "On the robustness of chaos in dynamical systems: Theories and applications, " Front. Phys. China 3, 195-204.
    • (2008) Front. Phys. China , vol.3 , pp. 195-204
    • Elhadj, Z.1    Sprott, J.C.2
  • 17
    • 35949019576 scopus 로고
    • Analysis of flow hysteresis by a one-dimensional map
    • Fraser, S. & Kapral, R. [1982] "Analysis of flow hysteresis by a one-dimensional map, " Phys. Rev. A 25, 3223-3233.
    • (1982) Phys. Rev. A , vol.25 , pp. 3223-3233
    • Fraser, S.1    Kapral, R.2
  • 18
    • 54749091683 scopus 로고    scopus 로고
    • Multistability, phase diagrams, and intransitivity in the lorenz-84 low-order atmospheric circulation model
    • Freire, J. G., Bonatto, C., DaCamara, C. & Gallas, J. A. C. [2008] "Multistability, phase diagrams, and intransitivity in the Lorenz-84 low-order atmospheric circulation model, " Chaos 18, 033121.
    • (2008) Chaos , vol.18 , pp. 033121
    • Freire, J.G.1    Bonatto, C.2    DaCamara, C.3    Gallas, J.A.C.4
  • 20
    • 68249126547 scopus 로고    scopus 로고
    • Relative abundance and structure of chaotic behavior: The nonpolynomial belousov-zhabotinsky reaction kinetics
    • Freire, J. G., Gallas, J. A. C. & Field, R. J. [2009] "Relative abundance and structure of chaotic behavior: The nonpolynomial Belousov-Zhabotinsky reaction kinetics, " J. Chem. Phys. 131, 044105.
    • (2009) J. Chem. Phys. , vol.131 , pp. 044105
    • Freire, J.G.1    Gallas, J.A.C.2    Field, R.J.3
  • 21
    • 0001404303 scopus 로고
    • Structure of the parameter space of the hénon map
    • Gallas, J. A. C. [1993] "Structure of the parameter space of the Hénon map, " Phys. Rev. Lett. 70, 2714-2717.
    • (1993) Phys. Rev. Lett. , vol.70 , pp. 2714-2717
    • Gallas, J.A.C.1
  • 22
    • 28844508668 scopus 로고
    • Dissecting shrimps: Results for some one-dimensional physical systems
    • Gallas, J. A. C. [1994] "Dissecting shrimps: results for some one-dimensional physical systems, " Physica A 202, 196-223.
    • (1994) Physica A , vol.202 , pp. 196-223
    • Gallas, J.A.C.1
  • 23
    • 0029209023 scopus 로고
    • Structure of the parameter space of a ring cavity
    • ", Special issue dedicated to the 60th birthday of Herbert Walther
    • Gallas, J. A. C. [1995] "Structure of the parameter space of a ring cavity, " Appl. Phys. B 60, S203-S213. Special issue dedicated to the 60th birthday of Herbert Walther;
    • (1995) Appl. Phys. B , vol.60
    • Gallas, J.A.C.1
  • 24
    • 0009952552 scopus 로고
    • Lyapunov exponents for a duffing oscillator
    • see also, &, ", "
    • see also Zeni, A. R. & Gallas, J. A. C. [1995] "Lyapunov exponents for a Duffing oscillator, " Physica D 89, 71-82.
    • (1995) Physica D , vol.89 , pp. 71-82
    • Zeni, A.R.1    Gallas, J.A.C.2
  • 25
    • 0001768333 scopus 로고
    • What can we learn from homoclinic orbits in chaotic dynamics?
    • Gaspard, P. & Nicolis, G. [1983] "What can we learn from homoclinic orbits in chaotic dynamics?" J. Stat. Phys. 31, 499-518.
    • (1983) J. Stat. Phys. , vol.31 , pp. 499-518
    • Gaspard, P.1    Nicolis, G.2
  • 26
    • 0021442615 scopus 로고
    • Bifurcation phenomena near homoclinic systems: A twoparameter analysis
    • Gaspard, P., Kapral, R. & Nicolis, G. [1984] "Bifurcation phenomena near homoclinic systems: A twoparameter analysis, " J. Stat. Phys. 35, 697-727. (Pubitemid 15454501)
    • (1984) Journal of Statistical Physics , vol.35 , Issue.5-6 , pp. 697-727
    • Gaspard, P.1    Kapral, R.2    Nicolis, G.3
  • 27
    • 34250127220 scopus 로고
    • T-points: A codimension two heteroclinic bifurcation
    • Glendinning, P. & Sparrow, C. [1986] "T-points: A codimension two heteroclinic bifurcation, " J. Stat. Phys. 43, 479-488.
    • (1986) J. Stat. Phys. , vol.43 , pp. 479-488
    • Glendinning, P.1    Sparrow, C.2
  • 29
    • 11744328036 scopus 로고
    • A three-variable model of deterministic chaos in the belousov-zhabotinsky reaction
    • Györgyi, L. & Field, R. J. [1992] "A three-variable model of deterministic chaos in the Belousov-Zhabotinsky reaction, " Nature 355, 808-810.
    • (1992) Nature , vol.355 , pp. 808-810
    • Györgyi, L.1    Field, R.J.2
  • 30
    • 0021768729 scopus 로고
    • A model of neuronal bursting using three coupled first order differential equations
    • Hindmarsh, J. L. & Rose, R. M. [1984] "A model of neuronal bursting using three coupled first order differential equations, " Proc. Royal Soc. London B 221, 87-102.
    • (1984) Proc. Royal Soc. London B , vol.221 , pp. 87-102
    • Hindmarsh, J.L.1    Rose, R.M.2
  • 32
    • 0004125699 scopus 로고
    • (Longmans, Green and Co., London), reprinted since 1956 by Dover, Mineola
    • Ince, E. L. [1926] Ordinary Differential Equations, (Longmans, Green and Co., London), reprinted since 1956 by Dover, Mineola
    • (1926) Ordinary Differential Equations
    • Ince, E.L.1
  • 33
    • 0000775434 scopus 로고
    • Fractal transformation of the 1d chaos produced by logarithmic map
    • Kawabe, T. & Kondo, Y. [1991a] "Fractal transformation of the 1d chaos produced by logarithmic map, " Prog. Theor. Phys. 85, 759-769.
    • (1991) Prog. Theor. Phys. , vol.85 , pp. 759-769
    • Kawabe, T.1    Kondo, Y.2
  • 34
    • 0038929736 scopus 로고
    • Intermittent chaos generated by logarithmic map
    • Kawabe, T. & Kondo, Y. [1991b] "Intermittent chaos generated by logarithmic map, " Prog. Theor. Phys. 86, 581-586.
    • (1991) Prog. Theor. Phys. , vol.86 , pp. 581-586
    • Kawabe, T.1    Kondo, Y.2
  • 35
    • 21144476891 scopus 로고
    • Bifurcations of the complex logarithmic map
    • Kawabe, T. & Kondo, Y. [1993] "Bifurcations of the complex logarithmic map, " J. Phys. Soc. Japan 62, 497-505.
    • (1993) J. Phys. Soc. Japan , vol.62 , pp. 497-505
    • Kawabe, T.1    Kondo, Y.2
  • 36
    • 45049083940 scopus 로고    scopus 로고
    • Compound windows of the hénon map
    • Lorenz, E. N. [2008] "Compound windows of the Hénon map, " Physica D 237, 1689-1704.
    • (2008) Physica D , vol.237 , pp. 1689-1704
    • Lorenz, E.N.1
  • 37
    • 43949159589 scopus 로고
    • Robust chaos in dynamic optimization models
    • Majumdar, M. & Mitra, T. [1994] "Robust chaos in dynamic optimization models, " Ricerche Economiche 48, 225-240.
    • (1994) Ricerche Economiche , vol.48 , pp. 225-240
    • Majumdar, M.1    Mitra, T.2
  • 38
    • 51149106106 scopus 로고    scopus 로고
    • Multistability, phase diagrams and statistical properties of the kicked rotor: A map with many coexisting attractors
    • Martins, L. C. & Gallas, J. A. C. [2008] "Multistability, phase diagrams and statistical properties of the kicked rotor: a map with many coexisting attractors, " Int. J. Bifurcation and Chaos 18, 1705-1717.
    • (2008) Int. J. Bifurcation and Chaos , vol.18 , pp. 1705-1717
    • Martins, L.C.1    Gallas, J.A.C.2
  • 39
    • 0842264193 scopus 로고    scopus 로고
    • Engineering complex systems
    • Ottino, J. M. [2004] "Engineering complex systems, " Nature 427, 399.
    • (2004) Nature , vol.427 , pp. 399
    • Ottino, J.M.1
  • 41
    • 0034636651 scopus 로고    scopus 로고
    • Robust chaos generation by a perceptron
    • Priel, A. & Kanter, I. [2000] "Robust chaos generation by a perceptron, " Europhys. Lett. 51, 230-236.
    • (2000) Europhys. Lett. , vol.51 , pp. 230-236
    • Priel, A.1    Kanter, I.2
  • 42
    • 68249102217 scopus 로고    scopus 로고
    • Estructura del espacio de parametros para las ecuaciones del circuito de chua
    • Available online from
    • Ramírez-Ávila, G. M. & Gallas, J. A. C. [2008] "Estructura del espacio de parametros para las ecuaciones del circuito de Chua, " Revista Boliviana de Fisica 14, 1-9; Available online from http://www.if.ufrgs.br/~jgallas
    • (2008) Revista Boliviana De Fisica , vol.14 , pp. 1-9
    • Ramírez-Ávila, G.M.1    Gallas, J.A.C.2
  • 43
    • 77951573144 scopus 로고    scopus 로고
    • Quantification of regular and chaotic oscillations in chua's circuit with piecewise-linear and cubic terms
    • in
    • Ramírez-Ávila, G. M. & Gallas, J. A. C. [2009] "Quantification of regular and chaotic oscillations in Chua's circuit with piecewise-linear and cubic terms, " in preparation.
    • (2009) Preparation
    • Ramírez-Ávila, G.M.1    Gallas, J.A.C.2
  • 44
    • 49549126801 scopus 로고
    • An equation for continuous chaos
    • Rössler, O. E. [1976] "An equation for continuous chaos, " Phys. Lett. A 57, 397-398.
    • (1976) Phys. Lett. A , vol.57 , pp. 397-398
    • Rössler, O.E.1
  • 45
    • 84985456277 scopus 로고
    • Continuous chaos: Four prototype equations
    • Rössler, O. E. [1979a] "Continuous chaos: four prototype equations, " Ann. N Y Acad. Sci. 316, 376-392.
    • (1979) Ann. N Y Acad. Sci. , vol.316 , pp. 376-392
    • Rössler, O.E.1
  • 46
    • 0000548789 scopus 로고
    • An equation for hyperchaos
    • Rössler, O. E. [1979b] "An equation for hyperchaos, " Phys. Lett. A 71, 155-157.
    • (1979) Phys. Lett. A , vol.71 , pp. 155-157
    • Rössler, O.E.1
  • 48
    • 0000764166 scopus 로고
    • On bifurcations of the lorenz attractor in the shimizu-morioka model
    • Shilnikov, A. L. [1993] "On bifurcations of the Lorenz attractor in the Shimizu-Morioka model, " Physica D 62, 338-346.
    • (1993) Physica D , vol.62 , pp. 338-346
    • Shilnikov, A.L.1
  • 50
    • 0031185630 scopus 로고    scopus 로고
    • Homoclinic phenomena in laser models
    • Shilnikov, A. L. [1997] "Homoclinic phenomena in laser models, " Comput. Math. Appl. 34, 245-251.
    • (1997) Comput. Math. Appl. , vol.34 , pp. 245-251
    • Shilnikov, A.L.1
  • 52
    • 77951602156 scopus 로고    scopus 로고
    • Global structure of periodicity hubs in lyapunov phase diagrams of dissipative flows
    • Vitolo, R., Glendinning, P. & Gallas, J. A. C. [2009] "Global structure of periodicity hubs in Lyapunov phase diagrams of dissipative flows, " preprint.
    • (2009) Preprint
    • Vitolo, R.1    Glendinning, P.2    Gallas, J.A.C.3


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.