Two New Asymmetric Boolean Chaos Oscillators with No Dependence on Incommensurate Time-Delays and Their Circuit Implementation
This manuscript introduces two new chaotic oscillators based on autonomous Boolean networks (ABN), preserving asymmetrical logic functions. That means that the ABNs require a combination of XOR-XNOR logic functions. We demonstrate analytically that the two ABNs do not have fixed points, and therefor...
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| Veröffentlicht in: | Symmetry (Basel) 2020-04, Vol.12 (4), p.506 |
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| container_title | Symmetry (Basel) |
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| creator | Munoz-Pacheco, Jesus M. García-Chávez, Tonatiuh Gonzalez-Diaz, Victor R. de La Fuente-Cortes, Gisela del Carmen Gómez-Pavón, Luz del Carmen |
| description | This manuscript introduces two new chaotic oscillators based on autonomous Boolean networks (ABN), preserving asymmetrical logic functions. That means that the ABNs require a combination of XOR-XNOR logic functions. We demonstrate analytically that the two ABNs do not have fixed points, and therefore, can evolve to Boolean chaos. Using the Lyapunov exponent’s method, we also prove the chaotic behavior, generated by the proposed chaotic oscillators, is insensitive to incommensurate time-delays paths. As a result, they can be implemented using distinct electronic circuits. More specifically, logic-gates–, GAL–, and FPGA–based implementations verify the theoretical findings. An integrated circuit using a CMOS 180nm fabrication technology is also presented to get a compact chaos oscillator with relatively high-frequency. Dynamical behaviors of those implementations are analyzed using time-series, time-lag embedded attractors, frequency spectra, Poincaré maps, and Lyapunov exponents. |
| doi_str_mv | 10.3390/sym12040506 |
| format | Article |
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| source | MDPI - Multidisciplinary Digital Publishing Institute; Elektronische Zeitschriftenbibliothek - Frei zugängliche E-Journals |
| subjects | Asymmetry Behavior Boolean Boolean algebra Boolean functions Chaos theory Circuits CMOS Electronic circuits Field programmable gate arrays Frequency spectrum Gates (circuits) Integrated circuits Liapunov exponents Logic Oscillators Poincare maps Time dependence |
| title | Two New Asymmetric Boolean Chaos Oscillators with No Dependence on Incommensurate Time-Delays and Their Circuit Implementation |
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