Opposition to Synchronization of Bistable State in Motif Configuration of Rössler Chaotic Oscillator Systems
Yıl 2024,
Cilt: 6 Sayı: 2, 131 - 143, 30.06.2024
Juan Hugo García López
Rider Jaimes-reategui
Guillermo Huerta-cuellar
Dıdıer Lopez Mancılla
Öz
This paper presents the study of the opposition to the synchronization of bistable chaotic oscillator systems in basic motif configurations. The following configurations were analyzed: Driver-response oscillator systems coupling, two driver oscillator systems to one response oscillator, and a three-oscillator systems ring unidirectional configuration. The study was conducted using the differential equations representing the piecewise linear Rössler-like electronic circuits; the initial conditions were changed to achieve a bistable characteristic Homoclinic H-type or Rössler R-type attractor. Analyzing a sweep of the initial conditions, the basin attractor was obtained. It can be observed that each system has a preferred Homoclinic chaotic attractor with any perturbation or change in initial conditions. A similarity analysis based on the coupling factor was also performed and found that the system has a preferentially Homoclinic chaotic attractor.
Destekleyen Kurum
CONAHCyT
Teşekkür
The authors acknowledge the support of the CONAHCyT
Kaynakça
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synchronization for multistable systems. IEEE Transactions
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Monograph series on nonlinear science and complexity 6: 1–239.
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for synchronization of coupled dynamical systems. Physical
Review E 63: 066219.
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2018 Synchronization: from coupled systems to complex networks.
Cambridge University Press.
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in coupled dynamical systems. Pramana 93: 1–13.
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synchronous states of two pendulum clocks suspended
on a swinging support. Mechanical Systems and Signal Processing
154: 107549.
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excitable medium. Nature 419: 131–132.
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and delayed recurrent loops. Physical Review Letters 76: 708.
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J. Cárdenas-Valdez, and E. Tlelo-Cuautle, 2020 Randomness
improvement of chaotic maps for image encryption in a wireless
communication scheme using pic-microcontroller via zigbee
channels. Chaos, Solitons and Fractals 133: 109646.
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in coupled chaotic oscillators: Toward a new criterion
for high-quality synchronization. Physical Review Letters 77:
1751.
- Khan, M. A., G. Mahapatra, J. K. Sarkar, and S. D. Jabeen, 2021
Design of multistability of chaotic systems via self and cross
coupling. The European Physical Journal Plus 136: 1–12.
- Khan, M. A., M. Nag, and S. Poria, 2017 Design of multistable
systems via partial synchronization. Pramana 89: 1–8.
- Liu, W., J. Xiao, X. Qian, and J. Yang, 2006 Antiphase synchronization
in coupled chaotic oscillators. Physical Review E 73:
057203.
- Maurer, J. and A. Libchaber, 1980 Effect of the prandtl number on
the onset of turbulence in liquid 4he. Journal de Physique lettres
41: 515–518.
- Méndez-Ramírez, R., A. Arellano-Delgado, and M. Á. Murillo-
Escobar, 2023 Network synchronization of macm circuits and its
application to secure communications. Entropy 25: 688.
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2021 On multistability near the boundary of generalized
synchronization in unidirectionally coupled chaotic systems.
Chaos: An Interdisciplinary Journal of Nonlinear Science 31:
083106.
- Pecora, L. M. and T. L. Carroll, 1990 Synchronization in chaotic
systems. Physical review letters 64: 821.
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concept in nonlinear sciences. Self 2: 3.
- Pisarchik, A., R. Jaimes-Reátegui, J. Villalobos-Salazar, J. Garcia-
Lopez, and S. Boccaletti, 2006 Synchronization of chaotic systems
with coexisting attractors. Physical review letters 96: 244102.
- Pisarchik, A. N. and R. Jaimes-Reategui, 2005 Intermittent lag synchronization
in a nonautonomous system of coupled oscillators.
Physics Letters A 338: 141–149.
- Pisarchik, A. N., R. Jaimes-Reátegui, and J. García-López, 2008
Synchronization of multistable systems. International Journal of
Bifurcation and Chaos 18: 1801–1819.
- Pisarchik, A. N., A. V. Kir’yanov, Y. O. Barmenkov, and R. Jaimes-
Reátegui, 2005 Dynamics of an erbium-doped fiber laser with
pump modulation: theory and experiment. JOSA B 22: 2107–
2114.
- Pm, G. and T. Kapitaniak, 2017 Synchronization in coupled multistable
systems with hidden attractors. Mathematical Problems
in Engineering 2017.
- Pol, B. and J. v. d. Mark, 1927 Frequency demultiplication. Nature
120: 363–364.
- Rodríguez-Orozco, E., E. E. García-Guerrero, E. Inzunza-Gonzalez,
O. R. López-Bonilla, A. Flores-Vergara, et al., 2018 Fpga-based
chaotic cryptosystem by using voice recognition as access key.
Electronics 7.
- Rosenblum, M. and J. Kurths, 2003 Synchronization: a universal
concept in nonlinear science. Cambridge University Press.
- Rosenblum, M. G., A. S. Pikovsky, and J. Kurths, 1996 Phase synchronization
of chaotic oscillators. Physical review letters 76:
1804.
- Rosenblum, M. G., A. S. Pikovsky, and J. Kurths, 1997 From phase
to lag synchronization in coupled chaotic oscillators. Physical
Review Letters 78: 4193.
- Ruiz-Silva, A., H. Gilardi-Velázquez, and E. Campos, 2021 Emergence
of synchronous behavior in a network with chaotic multistable
systems. Chaos, Solitons & Fractals 151: 111263.
- Rulkov, N. F., M. M. Sushchik, L. S. Tsimring, and H. D. Abarbanel,
1995 Generalized synchronization of chaos in directionally coupled
chaotic systems. Physical Review E 51: 980.
- Sarosh, P., S. A. Parah, and G. M. Bhat, 2022 An efficient image
encryption scheme for healthcare applications. Multimedia Tools
and Applications 81: 7253–7270.
- Sharma, N. and E. Ott, 2000 Exploiting synchronization to combat
channel distortions in communication with chaotic systems.
International Journal of Bifurcation and Chaos 10: 777–785.
- Stewart, H. B., R. Ghaffari, C. Franciosi, and H. Swinney, 1986
Nonlinear dynamics and chaos: geometrical methods for engineers and
scientists. Wiley New York.
- Trujillo-Toledo, D., O. López-Bonilla, E. García-Guerrero,
J. Esqueda-Elizondo, J. Cárdenas-Valdez, et al., 2023 Real-time
medical image encryption for h-iot applications using improved
sequences from chaotic maps. Integration 90: 131–145.
- Vaidyanathan, S., K. Benkouider, and A. Sambas, 2022 A new multistable
jerk chaotic system, its bifurcation analysis, backstepping
control-based synchronization design and circuit simulation.
Archives of Control Sciences 32: 123.
Yıl 2024,
Cilt: 6 Sayı: 2, 131 - 143, 30.06.2024
Juan Hugo García López
Rider Jaimes-reategui
Guillermo Huerta-cuellar
Dıdıer Lopez Mancılla
Kaynakça
- Ahmed, H., R. Ushirobira, D. Efimov, and W. Perruquetti, 2016 Robust
synchronization for multistable systems. IEEE Transactions
on Automatic Control 61: 1625–1630.
- Boccaletti, S., 2008 The synchronized dynamics of complex systems.
Monograph series on nonlinear science and complexity 6: 1–239.
- Boccaletti, S., L. M. Pecora, and A. Pelaez, 2001 Unifying framework
for synchronization of coupled dynamical systems. Physical
Review E 63: 066219.
- Boccaletti, S., A. N. Pisarchik, C. I. Del Genio, and A. Amann,
2018 Synchronization: from coupled systems to complex networks.
Cambridge University Press.
- Brun, E., B. Derighetti, D. Meier, R. Holzner, and M. Ravani, 1985
Observation of order and chaos in a nuclear spin–flip laser. JOSA
B 2: 156–167.
- Buldú, J. M., T. Heil, I. Fischer, M. C. Torrent, and J. García-Ojalvo,
2006 Episodic synchronization via dynamic injection. Physical
review letters 96: 024102.
- Carroll, T. L. and L. M. Pecora, 1995 Nonlinear dynamics in circuits.
World Scientific.
- Chakraborty, P. and S. Poria, 2019 Extreme multistable synchronisation
in coupled dynamical systems. Pramana 93: 1–13.
- Dudkowski, D., K. Czołczy´ nski, and T. Kapitaniak, 2021 Multistable
synchronous states of two pendulum clocks suspended
on a swinging support. Mechanical Systems and Signal Processing
154: 107549.
- Farkas, I., D. Helbing, and T. Vicsek, 2002 Mexican waves in an
excitable medium. Nature 419: 131–132.
- Foss, J., A. Longtin, B. Mensour, and J. Milton, 1996 Multistability
and delayed recurrent loops. Physical Review Letters 76: 708.
- García-Guerrero, E., E. Inzunza-González, O. López-Bonilla,
J. Cárdenas-Valdez, and E. Tlelo-Cuautle, 2020 Randomness
improvement of chaotic maps for image encryption in a wireless
communication scheme using pic-microcontroller via zigbee
channels. Chaos, Solitons and Fractals 133: 109646.
- Gauthier, D. J. and J. C. Bienfang, 1996 Intermittent loss of synchronization
in coupled chaotic oscillators: Toward a new criterion
for high-quality synchronization. Physical Review Letters 77:
1751.
- Khan, M. A., G. Mahapatra, J. K. Sarkar, and S. D. Jabeen, 2021
Design of multistability of chaotic systems via self and cross
coupling. The European Physical Journal Plus 136: 1–12.
- Khan, M. A., M. Nag, and S. Poria, 2017 Design of multistable
systems via partial synchronization. Pramana 89: 1–8.
- Liu, W., J. Xiao, X. Qian, and J. Yang, 2006 Antiphase synchronization
in coupled chaotic oscillators. Physical Review E 73:
057203.
- Maurer, J. and A. Libchaber, 1980 Effect of the prandtl number on
the onset of turbulence in liquid 4he. Journal de Physique lettres
41: 515–518.
- Méndez-Ramírez, R., A. Arellano-Delgado, and M. Á. Murillo-
Escobar, 2023 Network synchronization of macm circuits and its
application to secure communications. Entropy 25: 688.
- Moskalenko, O. I., A. A. Koronovskii, A. O. Selskii, and E. V. Evstifeev,
2021 On multistability near the boundary of generalized
synchronization in unidirectionally coupled chaotic systems.
Chaos: An Interdisciplinary Journal of Nonlinear Science 31:
083106.
- Pecora, L. M. and T. L. Carroll, 1990 Synchronization in chaotic
systems. Physical review letters 64: 821.
- Pikovsky, A., M. Rosenblum, J. Kurths, et al., 2001 A universal
concept in nonlinear sciences. Self 2: 3.
- Pisarchik, A., R. Jaimes-Reátegui, J. Villalobos-Salazar, J. Garcia-
Lopez, and S. Boccaletti, 2006 Synchronization of chaotic systems
with coexisting attractors. Physical review letters 96: 244102.
- Pisarchik, A. N. and R. Jaimes-Reategui, 2005 Intermittent lag synchronization
in a nonautonomous system of coupled oscillators.
Physics Letters A 338: 141–149.
- Pisarchik, A. N., R. Jaimes-Reátegui, and J. García-López, 2008
Synchronization of multistable systems. International Journal of
Bifurcation and Chaos 18: 1801–1819.
- Pisarchik, A. N., A. V. Kir’yanov, Y. O. Barmenkov, and R. Jaimes-
Reátegui, 2005 Dynamics of an erbium-doped fiber laser with
pump modulation: theory and experiment. JOSA B 22: 2107–
2114.
- Pm, G. and T. Kapitaniak, 2017 Synchronization in coupled multistable
systems with hidden attractors. Mathematical Problems
in Engineering 2017.
- Pol, B. and J. v. d. Mark, 1927 Frequency demultiplication. Nature
120: 363–364.
- Rodríguez-Orozco, E., E. E. García-Guerrero, E. Inzunza-Gonzalez,
O. R. López-Bonilla, A. Flores-Vergara, et al., 2018 Fpga-based
chaotic cryptosystem by using voice recognition as access key.
Electronics 7.
- Rosenblum, M. and J. Kurths, 2003 Synchronization: a universal
concept in nonlinear science. Cambridge University Press.
- Rosenblum, M. G., A. S. Pikovsky, and J. Kurths, 1996 Phase synchronization
of chaotic oscillators. Physical review letters 76:
1804.
- Rosenblum, M. G., A. S. Pikovsky, and J. Kurths, 1997 From phase
to lag synchronization in coupled chaotic oscillators. Physical
Review Letters 78: 4193.
- Ruiz-Silva, A., H. Gilardi-Velázquez, and E. Campos, 2021 Emergence
of synchronous behavior in a network with chaotic multistable
systems. Chaos, Solitons & Fractals 151: 111263.
- Rulkov, N. F., M. M. Sushchik, L. S. Tsimring, and H. D. Abarbanel,
1995 Generalized synchronization of chaos in directionally coupled
chaotic systems. Physical Review E 51: 980.
- Sarosh, P., S. A. Parah, and G. M. Bhat, 2022 An efficient image
encryption scheme for healthcare applications. Multimedia Tools
and Applications 81: 7253–7270.
- Sharma, N. and E. Ott, 2000 Exploiting synchronization to combat
channel distortions in communication with chaotic systems.
International Journal of Bifurcation and Chaos 10: 777–785.
- Stewart, H. B., R. Ghaffari, C. Franciosi, and H. Swinney, 1986
Nonlinear dynamics and chaos: geometrical methods for engineers and
scientists. Wiley New York.
- Trujillo-Toledo, D., O. López-Bonilla, E. García-Guerrero,
J. Esqueda-Elizondo, J. Cárdenas-Valdez, et al., 2023 Real-time
medical image encryption for h-iot applications using improved
sequences from chaotic maps. Integration 90: 131–145.
- Vaidyanathan, S., K. Benkouider, and A. Sambas, 2022 A new multistable
jerk chaotic system, its bifurcation analysis, backstepping
control-based synchronization design and circuit simulation.
Archives of Control Sciences 32: 123.