Edge of Chaos Theory Resolves Smale Paradox

Ascoli, Alon; Demirkol, Ahmet Şamil; Tetzlaff, Ronald; Chua, Leon O.

doi:10.1109/tcsi.2021.3133627

Cited by 42 publications

(25 citation statements)

References 23 publications

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“…143 Recurring to the universal Theory of Local Activity and Edge of Chaos is necessary to explain the mechanisms behind the appearance of complex phenomena in any physical system, which has the possibility to exchange energy with the respective environment. 144 The recent availability of memristor nanoscale physical realizations, 145,146 blessed with the capability to feature a Negative Differential The simplest ever-reported bioinspired circuit, 148 which reproduces the counterintuitive diffusion-driven transition from quiescence to sustained oscillatory behavior, observed by Smale in an eight-order reaction-diffusion system from cellular biology, 149 through half the number of dynamical states, encoded in two capacitors and two locally active NaMLab memristors, 146 on the proviso that the two identical memristive Pearson-Anson cells are preliminarily poised on some common Edge of Chaos operating point before the diffusion path, enabling their diffusive interaction, is activated. The four degrees of freedom of the proposed fourth-order RD-MCNN are encoded in the memristors' states x 1 and x 2 , and in the capacitors' voltages v Resistance (NDR), 147 which is a signature for Local Activity, enables the design of circuits, which, once some of their constitutive units are poised on the Edge of Chaos, may reproduce complex bifurcation phenomena, occurring in biological systems, while utilizing a lower number of degrees of freedom than their original counterparts.…”

Section: Edge Of Chaos-induced Bifurcations In Biomimetic Locally Act...mentioning

confidence: 99%

Recent Advances and Future Prospects for Memristive Materials, Devices, and Systems

et al. 2023

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Memristive technology has been rapidly emerging as a potential alternative to traditional CMOS technology, which is facing fundamental limitations in its development. Since oxide-based resistive switches were demonstrated as memristors in 2008, memristive devices have garnered significant attention due to their biomimetic memory properties, which promise to significantly improve power consumption in computing applications. Here, we provide a comprehensive overview of recent advances in memristive technology, including memristive devices, theory, algorithms, architectures, and systems. In addition, we discuss research directions for various applications of memristive technology including hardware accelerators for artificial intelligence, in-sensor computing, and probabilistic computing. Finally, we provide a forward-looking perspective on the future of memristive technology, outlining the challenges and opportunities for further research and innovation in this field. By providing an up-to-date overview of the state-of-the-art in memristive technology, this review aims to inform and inspire further research in this field.

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Section: Edge Of Chaos-induced Bifurcations In Biomimetic Locally Act...mentioning

confidence: 99%

Recent Advances and Future Prospects for Memristive Materials, Devices, and Systems

et al. 2023

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“…(2) 0 . With some abuse of notation, we denote by x 0 (t) the solution with initial condition x(t 0 ) = x 0 and input u as in (38). We suppose that at t = t 1 such a solution lies onto the attractor corresponding to the constant input U…”

Section: Extension To Non-constant Inputs Umentioning

confidence: 99%

“…The multistability feature of memristors has been thoroughly investigated, also in connection with some classic problems (see, e.g., [38], [39]). However, several interesting issues still deserve to be analyzed.…”

Section: Introductionmentioning

confidence: 99%

Embedding the Dynamics of Forced Nonlinear Systems in Multistable Memristor Circuits

Innocenti

Tesi

Marco

et al. 2022

IEEE J. Emerg. Sel. Topics Circuits Syst.

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A well-known feature of memristors is that they makes the circuit dynamics much richer than that generated by classical RLC circuits containing nonlinear resistors. In the case of circuits with ideal memristors, such a multistability property, i.e., the coexistence of many different attractors for a fixed set of parameters, is connected to the fact that the state space is composed of a continuum of invariant manifolds where either convergent or oscillatory and more complex behaviors can be displayed. In this paper we investigate the possibility of designing memristor circuits where known attractors are embedded into the invariant manifolds. We consider a class of forced nonlinear systems containing several systems which are known to display complex dynamics, and we investigate under which conditions the dynamics of any given system of the class can be reproduced by a circuit composed of a two-terminal (one port) element connected to a flux-controlled memristor. It is shown that an input-less circuit is capable to replicate the system attractors generated by varying the constant forcing input, once the parameters of the two-terminal element and the memristor nonlinear characteristic are suitably selected. Indeed, there is a one-one correspondence between the dynamics generated by the nonlinear system for a constant value of the input and that displayed on one of the invariant manifolds of the input-less memristor circuit. Some extensions concerning the case of non-constant forcing terms and the use of charge-controlled memristors are also provided. The results are illustrated via FitzHugh-Nagumo model and Duffing oscillator.

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“…Aimed at the nonlinear system solution, the Runge Kutta 4th order (RK4) method, multi‐step differential transform [ 10 ] and two‐point block methods [ 11 ] are considered. Besides, the chaos edge theory [ 12 ] is also proposed in resolving the Smale paradox, where complex behaviors including the static and dynamic pattern formulation emerging in the bio‐inspired array can reproduce shocking phenomenon when investigating a chaotic model from cellular biology. To overcome the chaos disappearance caused by parameter disturbance in practical applications, many new chaotic models and nonlinear systems [ 13,14 ] are proposed including the transient chaos, [ 15 ] spatial chaos, [ 16 ] topological chaos, [ 17 ] mixed multi‐chaos, [ 18 ] 3D pulsed chaos.…”

Section: Introductionmentioning

confidence: 99%

Natural Exponential and Three‐Dimensional Chaotic System

et al. 2023

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Existing chaotic system exhibits unpredictability and nonrepeatability in a deterministic nonlinear architecture, presented as a combination of definiteness and stochasticity. However, traditional two-dimensional chaotic systems cannot provide sufficient information in the dynamic motion and usually feature low sensitivity to initial system input, which makes them computationally prohibitive in accurate time series prediction and weak periodic component detection. Here, a natural exponential and three-dimensional chaotic system with higher sensitivity to initial system input conditions showing astonishing extensibility in time series prediction and image processing is proposed. The chaotic performance evaluated theoretically and experimentally by Poincare mapping, bifurcation diagram, phase space reconstruction, Lyapunov exponent, and correlation dimension provides a new perspective of nonlinear physical modeling and validation. The complexity, robustness, and consistency are studied by recursive and entropy analysis and comparison. The method improves the efficiency of time series prediction, nonlinear dynamics-related problem solving and expands the potential scope of multi-dimensional chaotic systems.

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Edge of Chaos Theory Resolves Smale Paradox

Cited by 42 publications

References 23 publications

Recent Advances and Future Prospects for Memristive Materials, Devices, and Systems

Recent Advances and Future Prospects for Memristive Materials, Devices, and Systems

Embedding the Dynamics of Forced Nonlinear Systems in Multistable Memristor Circuits

Natural Exponential and Three‐Dimensional Chaotic System

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