A novel no-equilibrium HR neuron model with hidden homogeneous extreme multistability. (English) Zbl 1498.92020
Summary: In this paper, a novel no-equilibrium Hindmarsh-Rose (HR) neuron model with memristive electromagnetic induction is proposed. This memristive HR neuron model exhibits complex memristor initial offset boosting dynamics, from which infinitely many coexisting hidden attractors sharing the same shape but with different positions can be generated, therefore breeding the interesting phenomenon of hidden homogeneous extreme multistability. The complicated dynamical behaviors are detailedly investigated via bifurcation diagrams, Lyapunov exponents, time series, attraction basins and spectral entropy (SE) complexity. Moreover, PSIM circuit simulations and DSP hardware experiments are carried out to demonstrate the theoretical analyses and numerical simulations. Finally, a pseudorandom number generator is also designed by using the memristor initial-controlled chaotic sequences extracted from the memristive HR neuron model. The performance analysis results show that these chaotic sequences can yield pseudorandom numbers with excellent randomness, which are more suitable for chaos-based engineering applications.
MSC:
| 92B20 | Neural networks for/in biological studies, artificial life and related topics |
| 34C60 | Qualitative investigation and simulation of ordinary differential equation models |
| 94A12 | Signal theory (characterization, reconstruction, filtering, etc.) |
Keywords:
memristive HR neuron model; initial offset boosting; homogeneous multistability; initial-controlled chaotic sequence; pseudorandom number generatorReferences:
| [1] | Lv, M.; Wang, C.; Ren, G. D.; Ma, J., Model of electrical activity in a neuron under magnetic flow effect, Nonlinear Dynamics, 85, 3, 1479-1490 (2016) |
| [2] | Lv, M.; Ma, J., Multiple modes of electrical activities in a new neuron model under electromagnetic radiation, Neurocomputing, 205, 3, 375-381 (2016) |
| [3] | Hodgkin, A. L.; Huxley, A. F., A quantitative description of membrane current and its application to conduction and excitation in nerve, The Journal of Physiology, 117, 4, 500-544 (1952) |
| [4] | Morris, C.; Lecar, H., Voltage oscillations in the barnacle giant muscle fiber, Biophysical Journal, 35, 1, 193-213 (1981) |
| [5] | Hindmarsh, J. L.; Rose, R. M., A model of the nerve impulse using two first-order differential equations, Nature, 296, 5853, 162-164 (1982) |
| [6] | Hindmarsh, J. L.; Rose, R. M., A model of neuronal bursting using three coupled first order differential equations, Proceedings of The Royal Society B: Biological Sciences, 221, 1222, 87-102 (1984) |
| [7] | Innocenti, G.; Morelli, A.; Genesio, R.; Torcini, A., Dynamical phases of the hindmarsh-rose neuronal model: Studies of the transition from bursting to spiking chaos, Chaos, 17, 4, 043128 (2007) · Zbl 1163.37336 |
| [8] | Gonzalezmiranda, J. M., Observation of a continuous interior crisis in the hindmarsh-rose neuron model, Chaos, 13, 3, 845-852 (2003) · Zbl 1080.92505 |
| [9] | Bao, B.; Hu, A.; Xu, Q.; Bao, H.; Wu, H.; Chen, M., AC-induced coexisting asymmetric bursters in the improved hindmarsh-rose model, Nonlinear Dynamics, 92, 4, 1695-1706 (2018) |
| [10] | ZandiMehran, N.; Jafari, S.; Golpayegani, S. M.R. H.; Nazarimehr, F.; Perc, M., Different synaptic connections evoke different firing patterns in neurons subject to an electromagnetic field, Nonlinear Dynamics, 100, 2, 1809-1824 (2020) |
| [11] | Wu, K.; Luo, T.; Lu, H.; Wang, Y., Bifurcation study of neuron firing activity of the modified hindmarsh-rose model, Neural Computing and Applications, 27, 3, 739-747 (2016) |
| [12] | Ngouonkadi, E. B.M.; Fotsin, H. B.; Fotso, P. L.; Tamba, V. K.; Cerdeira, H. A., Bifurcations and multistability in the extended hindmarsh-rose neuronal oscillator, Chaos Solitons Fractals, 85, 4, 151-163 (2016) · Zbl 1355.34078 |
| [13] | Bao, B.; Hu, A.; Bao, H.; Xu, Q.; Chen, M.; Wu, H., Three-dimensional memristive hindmarsh-rose neuron model with hidden coexisting asymmetric behaviors, Complexity, 2018, 2, 1-11 (2018) |
| [14] | Bao, H.; Hu, A.; Liu, W.; Bao, B., Hidden bursting firings and bifurcation mechanisms in memristive neuron model with threshold electromagnetic induction, IEEE Transactions on Neural Networks, 31, 2, 502-511 (2020) |
| [15] | Lin, H.; Wang, C.; Sun, Y.; Yao, W., Firing multistability in a locally active memristive neuron model, Nonlinear Dynamics, 100, 5, 3667-3683 (2020) |
| [16] | Lai, Q.; Norouzi, B.; Liu, F., Dynamic analysis, circuit realization, control design and image encryption application of an extended lü system with coexisting attractors, Chaos Solitons Fractals, 114, 12, 230-245 (2018) · Zbl 1415.34079 |
| [17] | Wang, N.; Zhang, G.; Ren, L.; Bao, H., Coexisting asymmetric behavior and free control in a simple 3-d chaotic system, AEU-International Journal of Electronics and Communications, 122, 7, 153234 (2020) |
| [18] | Jahanshahi, H.; Yousefpour, A.; Wei, Z.; Alcaraz, R.; Bekiros, S., A financial hyperchaotic system with coexisting attractors: Dynamic investigation, entropy analysis, control and synchronization, Chaos Solitons Fractals, 126, 9, 66-77 (2019) · Zbl 1451.91233 |
| [19] | Yuan, F.; Li, Y., A chaotic circuit constructed by a memristor, a memcapacitor and a meminductor, Chaos, 29, 10, 101101 (2019) · Zbl 1425.94088 |
| [20] | Li, C.; Thio, W. J.; Iu, H. H.; Lu, T., A memristive chaotic oscillator with increasing amplitude and frequency, IEEE Access, 6, 12, 12945-12950 (2018) |
| [21] | Gu, J.; Li, C.; Chen, Y.; Iu, H. H.; Lei, T., A conditional symmetric memristive system with infinitely many chaotic attractors, IEEE Access, 8, 1, 12394-12401 (2020) |
| [22] | Bao, B.; Li, H. Z.; Zhu, L.; Zhang, X.; Chen, M., Initial-switched boosting bifurcations in 2d hyperchaotic map, Chaos, 30, 3, 033107 (2020) · Zbl 1445.37028 |
| [23] | Zhang, L. P.; Liu, Y.; Wei, Z. C.; Jiang, H. B.; Bi, Q. S., A novel class of two-dimensional chaotic maps with infinitely many coexisting attractors, Chinese Physics B, 29, 6, 060501 (2020) |
| [24] | Breakspear, M., Dynamic models of large-scale brain activity, Nature Neuroscience, 20, 3, 340-352 (2017) |
| [25] | Kwan, P.; Brodie, M. J., Early identification of refractory epilepsy, New England Journal of Medicine, 342, 5, 314-319 (2000) |
| [26] | Sandyk, R., Alzheimer’s disease: improvement of visual memory and visuoconstructive performance by treatment with picotesla range magnetic fields, International journal of neuroscience, 76, 3-4, 185-225 (1994) |
| [27] | Chen, M.; Ren, X.; Huagan, W. U.; Quan, X. U.; Bao, B., Periodically varied initial offset boosting behaviors in a memristive system with cosine memductance, Frontiers of Information Technology Electronic Engineering, 20, 12, 1706-1716 (2019) |
| [28] | Zheng, Z.; Lü, J.; Chen, G.; Zhou, T.; Zhang, S., Generating two simultaneously chaotic attractors with a switching piecewise-linear controller, Chaos, Solitons Fractals, 20, 2, 277-288 (2004) · Zbl 1045.37018 |
| [29] | Leonov, G. A.; Kuznetsov, N. V.; Mokaev, T. N., Homoclinic orbits, and self-excited and hidden attractors in a lorenz-like system describing convective fluid motion, The European Physical Journal Special Topics, 224, 8, 1421-1458 (2015) |
| [30] | Nik, H. S.; Effati, S.; Saberi-Nadjafi, J. A.F. A.R., Ultimate bound sets of a hyperchaotic system and its application in chaos synchronization, Complexity, 20, 4, 30-44 (2015) |
| [31] | Dudkowski, D.; Jafari, S.; Kapitaniak, T.; Kuznetsov, N. V.; Leonov, G. A.; Prasad, A., Hidden attractors in dynamical systems, Physics Reports, 637, 6, 1-50 (2016) · Zbl 1359.34054 |
| [32] | Jafari, S.; Sprott, J. C.; Golpayegani, S. M., Elementary quadratic chaotic flows with no equilibria, Physics Letters A, 377, 9, 699-702 (2013) · Zbl 1428.34059 |
| [33] | Wei, Z., Dynamical behaviors of a chaotic system with no equilibria, Physics Letters A, 376, 2, 102-108 (2011) · Zbl 1255.37013 |
| [34] | Vaidyanathan, S.; Sambas, A.; Mamat, M.; Sanjaya, W. M., A new three-dimensional chaotic system with a hidden attractor, circuit design and application in wireless mobile robot, Archives of Control Sciences, 27, 4, 541-554 (2017) · Zbl 1440.93176 |
| [35] | Peng, X.; Zeng, Y., Image encryption application in a system for compounding self-excited and hidden attractors, Chaos Solitons Fractals, 139, 10, 110044 (2020) · Zbl 1490.94024 |
| [36] | Gottwald, G. A.; Melbourne, I., On the validity of the 0-1 test for chaos, Nonlinearity, 22, 6, 1367-1382 (2009) · Zbl 1171.65091 |
| [37] | Wolf, A.; Swift, J. B.; Swinney, H. L.; Vastano, J. A., Determining lyapunov exponents from a time series, Physica D: Nonlinear Phenomena, 16, 3, 285-317 (1985) · Zbl 0585.58037 |
| [38] | Natiq, H.; Banerjee, S.; Said, M. R., Cosine chaotification technique to enhance chaos and complexity of discrete systems, The European Physical Journal-special Topics, 228, 1, 185-194 (2019) |
| [39] | Wang, L.; Sun, K.; Peng, Y.; He, S., Chaos and complexity in a fractional-order higher-dimensional multicavity chaotic map, Chaos Solitons Fractals, 131, 2, 109488 (2020) · Zbl 1495.39005 |
| [40] | He, S.; Sun, K.; Wang, H., Complexity analysis and DSP implementation of the fractional-order lorenz hyperchaotic system, Entropy, 17, 12, 8299-8311 (2015) |
| [41] | Wang, N.; Zhang, G.; Bao, H., Bursting oscillations and coexisting attractors in a simple memristor-capacitor-based chaotic circuit, Nonlinear Dynamics, 97, 2, 1477-1494 (2019) · Zbl 1430.94112 |
| [42] | Sun, K.; He, S.; He, Y.; Yin, L., Complexity analysis of chaotic pseudo-random sequences based on spectral entropy algorithm, Acta Physica Sinica, 62, 1, 27-34 (2013) |
| [43] | Wang, N.; Zhang, G.; Bao, H., A simple autonomous chaotic circuit with dead-zone nonlinearity, IEEE Transactions on Circuits and Systems II: Express Briefs, 67, 12, 3502-3506 (2020) |
| [44] | Wu, H.; Ye, Y.; Chen, M.; Xu, Q.; Bao, B., Periodically switched memristor initial boosting behaviors in memristive hypogenetic jerk system, IEEE Access, 7, 10, 145022-145029 (2019) |
| [45] | Njitacke, Z. T.; Kengne, J.; Kengne, L. K., Antimonotonicity, chaos and multiple coexisting attractors in a simple hybrid diode-based jerk circuit, Chaos Solitons Fractals, 105, 12, 77-91 (2017) |
| [46] | Tlelocuautle, E.; Diazmunoz, J. D.; Gonzalezzapata, A. M.; Li, R.; Leonsalas, W. D.; Fernandez, F. V.; Guillenfernandez, O.; Cruzvega, I., Chaotic image encryption using hopfield and hindmarsh-rose neurons implemented on FPGA, Sensors, 20, 5, 1326 (2020) |
| [47] | Rajagopal, K.; Nazarimehr, F.; Guessas, L.; Karthikeyan, A.; Srinivasan, A.; Jafari, S., Analysis, control and FPGA implementation of a fractional-order modified shinriki circuit, Journal of Circuits, Systems, and Computers, 28, 14, 1950232 (2019) |
| [48] | Wang, M.; Li, J.; Yu, S. S.; Zhang, X.; Li, Z.; Iu, H. H.C., A novel 3d non autonomous system with parametrically excited abundant dynamics and bursting oscillations, Chaos, 30, 4, 043125 (2020) · Zbl 1437.34051 |
| [49] | Ma, C.; Mou, J.; Yang, F.; Yan, H., A fractional-order hopfield neural network chaotic system and its circuit realization, European Physical Journal Plus, 135, 1, 1-16 (2020) |
| [50] | Ozdemir, A.; Pehlivan, I.; Akgul, A.; Guleryuz, E., A strange novel chaotic system with fully golden proportion equilibria and its mobile microcomputer-based RNG application, Chinese Journal of Physics, 56, 6, 2852-2864 (2018) |
| [51] | Nardo, L. G.; Nepomuceno, E. G.; Ariasgarcia, J.; Butusov, D. N., Image encryption using finite-precision error, Chaos Solitons Fractals, 123, 6, 69-78 (2019) · Zbl 1448.94218 |
| [52] | Rukhin, A.; Soto, J.; Nechvatal, J.; Smid, M.; Barker, E., A statistical test suite for random and pseudorandom number generators for cryptographic applications (2000) |
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