Please wait a minute...
Chin. Phys. B, 2013, Vol. 22(8): 080202    DOI: 10.1088/1674-1056/22/8/080202
GENERAL Prev   Next  

The dynamics of a symmetric coupling of three modified quadratic maps

Paulo C. Rech
Departamento de Física, Universidade do Estado de Santa Catarina, 89219-710 Joinville, Brazil
Abstract  We investigate the dynamical behavior of a symmetric linear coupling of three quadratic maps with exponential terms, and identify various interesting features as a function of two control parameters. In particular, we investigate the emergence of quasiperiodic states arising from Naimark-Sacker bifurcations of stable period-1, period-2, and period-3 orbits. We also investigate the multistability in the same coupling. Lyapunov exponents, parameter planes, phase space portraits, and bifurcation diagrams are used to investigate transitions from periodic to quasiperiodic states, from quasiperiodic to mode-locked states and to chaotic states, and from chaotic to hyperchaotic states.
Keywords:  Naimark-Sacker bifurcation      quasiperiodicity      chaos      hyperchaos  
Received:  22 October 2012      Revised:  26 January 2013      Accepted manuscript online: 
PACS:  02.30.Rz (Integral equations)  
  05.45.-a (Nonlinear dynamics and chaos)  
Fund: Project supported by Conselho Nacional de Desenvolvimento Científico e Tecnológico-CNPq, Brazil.
Corresponding Authors:  Paulo C. Rech     E-mail:  dfi2pcr@joinville.udesc.br

Cite this article: 

Paulo C. Rech The dynamics of a symmetric coupling of three modified quadratic maps 2013 Chin. Phys. B 22 080202

[1] Hénon M 1976 Commun. Math. Phys. 50 69
[2] Pando C L, Acosta G A L, Meucci R and Ciofini M 1995 Phys. Lett. A 199 191
[3] Zhou C S and Chen T L 1997 Phys. Lett. A 225 60
[4] Colli E, Piassi V S M, Tufaile A and Sartorelli J C 2004 Phys. Rev. E 70 066215
[5] Hassell M 1975 J. Anim. Ecol. 44 283
[6] Andrecut M and Kauffman S A 2007 Phys. Lett. A 367 281
[7] Ge H X 2011 Chin. Phys. B 20 090502
[8] Yuen C H and Wong K W 2012 Chin. Phys. B 21 010502
[9] Zhusubaliyev Z T and Mosekilde E 2003 Bifurcations and Chaos in Piecewise-Smooth Dynamical Systems (Singapore: World Scientific)
[10] Bao B C, Kang Z S, Xu J P and Hu W 2009 Acta Phys. Sin. 58 1420 (in Chinese)
[11] Wiggins S 2003 Introduction to Applied Nonlinear Dynamical Systems and Chaos (New York: Springer)
[12] Guckenheimer J and Holmes P 2002 Nonlinear Oscillations, Dynamical Systems, and Bifurcations of Vector Fields (New York: Springer)
[13] Li X F, Chu Y D and Zhang H 2012 Chin. Phys. B 21 030203
[14] Schuster H G and Just W 2005 Deterministic Chaos, an Introduction (Weinheim: WILEY-VCH)
[1] An incommensurate fractional discrete macroeconomic system: Bifurcation, chaos, and complexity
Abderrahmane Abbes, Adel Ouannas, and Nabil Shawagfeh. Chin. Phys. B, 2023, 32(3): 030203.
[2] A novel algorithm to analyze the dynamics of digital chaotic maps in finite-precision domain
Chunlei Fan(范春雷) and Qun Ding(丁群). Chin. Phys. B, 2023, 32(1): 010501.
[3] Memristor hyperchaos in a generalized Kolmogorov-type system with extreme multistability
Xiaodong Jiao(焦晓东), Mingfeng Yuan(袁明峰), Jin Tao(陶金), Hao Sun(孙昊), Qinglin Sun(孙青林), and Zengqiang Chen(陈增强). Chin. Phys. B, 2023, 32(1): 010507.
[4] Synchronously scrambled diffuse image encryption method based on a new cosine chaotic map
Xiaopeng Yan(闫晓鹏), Xingyuan Wang(王兴元), and Yongjin Xian(咸永锦). Chin. Phys. B, 2022, 31(8): 080504.
[5] Multi-target ranging using an optical reservoir computing approach in the laterally coupled semiconductor lasers with self-feedback
Dong-Zhou Zhong(钟东洲), Zhe Xu(徐喆), Ya-Lan Hu(胡亚兰), Ke-Ke Zhao(赵可可), Jin-Bo Zhang(张金波),Peng Hou(侯鹏), Wan-An Deng(邓万安), and Jiang-Tao Xi(习江涛). Chin. Phys. B, 2022, 31(7): 074205.
[6] Complex dynamic behaviors in hyperbolic-type memristor-based cellular neural network
Ai-Xue Qi(齐爱学), Bin-Da Zhu(朱斌达), and Guang-Yi Wang(王光义). Chin. Phys. B, 2022, 31(2): 020502.
[7] Energy spreading, equipartition, and chaos in lattices with non-central forces
Arnold Ngapasare, Georgios Theocharis, Olivier Richoux, Vassos Achilleos, and Charalampos Skokos. Chin. Phys. B, 2022, 31(2): 020506.
[8] Bifurcation and dynamics in double-delayed Chua circuits with periodic perturbation
Wenjie Yang(杨文杰). Chin. Phys. B, 2022, 31(2): 020201.
[9] Resonance and antiresonance characteristics in linearly delayed Maryland model
Hsinchen Yu(于心澄), Dong Bai(柏栋), Peishan He(何佩珊), Xiaoping Zhang(张小平), Zhongzhou Ren(任中洲), and Qiang Zheng(郑强). Chin. Phys. B, 2022, 31(12): 120502.
[10] An image encryption algorithm based on spatiotemporal chaos and middle order traversal of a binary tree
Yining Su(苏怡宁), Xingyuan Wang(王兴元), and Shujuan Lin(林淑娟). Chin. Phys. B, 2022, 31(11): 110503.
[11] Nonlinear dynamics analysis of cluster-shaped conservative flows generated from a generalized thermostatted system
Yue Li(李月), Zengqiang Chen(陈增强), Zenghui Wang(王增会), and Shijian Cang(仓诗建). Chin. Phys. B, 2022, 31(1): 010501.
[12] Dynamics analysis in a tumor-immune system with chemotherapy
Hai-Ying Liu(刘海英), Hong-Li Yang(杨红丽), and Lian-Gui Yang(杨联贵). Chin. Phys. B, 2021, 30(5): 058201.
[13] Control of chaos in Frenkel-Kontorova model using reinforcement learning
You-Ming Lei(雷佑铭) and Yan-Yan Han(韩彦彦). Chin. Phys. B, 2021, 30(5): 050503.
[14] Resistance fluctuations in superconducting KxFe2-ySe2 single crystals studied by low-frequency noise spectroscopy
Hai Zi(子海), Yuan Yao(姚湲), Ming-Chong He(何明冲), Di Ke(可迪), Hong-Xing Zhan(詹红星), Yu-Qing Zhao(赵宇清), Hai-Hu Wen(闻海虎), and Cong Ren(任聪). Chin. Phys. B, 2021, 30(4): 047402.
[15] A multi-directional controllable multi-scroll conservative chaos generator: Modelling, analysis, and FPGA implementation
En-Zeng Dong(董恩增), Rong-Hao Li(李荣昊), and Sheng-Zhi Du(杜升之). Chin. Phys. B, 2021, 30(2): 020505.
No Suggested Reading articles found!