Nonlinear Networks With Mem-Elements: Complex Dynamics via Flux–Charge Analysis Method
| العنوان: | Nonlinear Networks With Mem-Elements: Complex Dynamics via Flux–Charge Analysis Method |
|---|---|
| المؤلفون: | Fernando Corinto, Leon O. Chua, Mauro Di Marco, Mauro Forti |
| المصدر: | IEEE Transactions on Cybernetics. 50:4758-4771 |
| بيانات النشر: | Institute of Electrical and Electronics Engineers (IEEE), 2020. |
| سنة النشر: | 2020 |
| مصطلحات موضوعية: | nonlinear inductors and capacitors, 02 engineering and technology, Topology, Computer Science::Emerging Technologies, 0202 electrical engineering, electronic engineering, information engineering, Electrical and Electronic Engineering, Invariant (mathematics), Bifurcations without parameters, coexisting dynamics, flux-charge analysis, memcapacitor and meminductor, memristor, Physics, Artificial neural network, Basis (linear algebra), 020208 electrical & electronic engineering, Reservoir computing, Computer Science Applications, Human-Computer Interaction, Nonlinear system, Complex dynamics, Neuromorphic engineering, Control and Systems Engineering, Equivalent circuit, 020201 artificial intelligence & image processing, Software, Information Systems |
| الوصف: | Nonlinear dynamic memory elements, as memristors, memcapacitors, and meminductors (also known as mem-elements), are of paramount importance in conceiving the neural networks, mem-computing machines, and reservoir computing systems with advanced computational primitives. This paper aims to develop a systematic methodology for analyzing complex dynamics in nonlinear networks with such emerging nanoscale mem-elements. The technique extends the flux–charge analysis method (FCAM) for nonlinear circuits with memristors to a broader class of nonlinear networks $\boldsymbol {\mathcal{ N}} $ containing also memcapacitors and meminductors. After deriving the constitutive relation and equivalent circuit in the flux–charge domain of each two-terminal element in $\boldsymbol {\mathcal{ N}} $ , this paper focuses on relevant subclasses of $\boldsymbol {\mathcal{ N}} $ for which a state equation description can be obtained. On this basis, salient features of the dynamics are highlighted and studied analytically: 1) the presence of invariant manifolds in the autonomous networks; 2) the coexistence of infinitely many different reduced-order dynamics on manifolds; and 3) the presence of bifurcations due to changing the initial conditions for a fixed set of parameters (also known as bifurcations without parameters). Analytic formulas are also given to design nonautonomous networks subject to pulses that drive trajectories through different manifolds and nonlinear reduced-order dynamics. The results, in this paper, provide a method for a comprehensive understanding of complex dynamical features and computational capabilities in nonlinear networks with mem-elements, which is fundamental for a holistic approach in neuromorphic systems with such emerging nanoscale devices. |
| تدمد: | 2168-2275 2168-2267 |
| DOI: | 10.1109/tcyb.2019.2904903 |
| URL الوصول: | https://explore.openaire.eu/search/publication?articleId=doi_dedup___::bdcd48117000828b11b495ded484adc6 https://doi.org/10.1109/tcyb.2019.2904903 |
| Rights: | CLOSED |
| رقم الانضمام: | edsair.doi.dedup.....bdcd48117000828b11b495ded484adc6 |
| قاعدة البيانات: | OpenAIRE |
| تدمد: | 21682275 21682267 |
|---|---|
| DOI: | 10.1109/tcyb.2019.2904903 |