Edge Of Chaos Domain Research Articles

Biphasic action potential and chaos in a symmetrical Chua Corsage Memristor-based circuit.

Neuromorphic computing provides unique computing and memory capabilities that could break the limitation of conventional von Neumann computing. Toward realizing neuromorphic computing, fabrication and synthetization of hardware elements and circuits to emulate biological neurons are crucial. Despite the striking progress in exploring neuron circuits, the existing circuits can only reproduce monophasic action potentials, and no studies report on circuits that could emulate biphasic action potentials, limiting the development of neuromorphic devices. Here, we present a simple third-order memristive circuit built with a classical symmetrical Chua Corsage Memristor (SCCM) to accurately emulate biological neurons and show that the circuit can reproduce monophasic action potentials, biphasic action potentials, and chaos. Applying the edge of chaos criterion, we calculate that the SCCM and the proposed circuit have the symmetrical edge of chaos domains with respect to the origin, which plays an important role in generating biphasic action potentials. Also, we draw a parameter classification map of the proposed circuit, showing the edge of chaos domain (EOCD), the locally active domain, and the locally passive domain. Near the calculated EOCD, the third-order circuit generates monophasic action potentials, biphasic action potentials, chaos, and ten types of symmetrical bi-directional neuromorphic phenomena by only tuning the input voltage, showing a resemblance to biological neurons. Finally, a physical SCCM circuit and some experimentally measured neuromorphic waveforms are exhibited. The experimental results agree with the numerical simulations, verifying that the proposed circuit is suitable as artificial neurons.

Edge of Chaos Is Sine Qua Non for Turing Instability

Diffusion-driven instabilities with pattern formation may occur in a network of identical, regularly-spaced, and resistively-coupled cells if and only if the uncoupled cell is poised on a locally-active and stable operating point in the Edge of Chaos domain. This manuscript presents the simplest ever-reported two-cell neural network, combining together only 7 two-terminal components, namely 2 batteries, 3 resistors, and 2 volatile NbOx memristive threshold switches from NaMLab, and subject to diffusion-driven instabilities with the concurrent emergence of Turing patterns. Very remarkably, this is the first time an homogeneous cellular medium, with no other dynamic element than 2 locally-active memristors, hence the attribute all-memristor coined to address it in this paper, is found to support complex phenomena. The destabilization of the homogeneous solution occurs in this second-order two-cell array if and only if the uncoupled cell circuit parameters are chosen from the Edge of Chaos domain. A deep circuit- and system-theoretic investigation, including linearization analysis and phase portrait investigation, provides a comprehensive picture for the local and global dynamics of the bio-inspired network, revealing how a theory-assisted approach may guide circuit design with inherently non-linear memristive devices.

Edge of Chaos in Memristor Cellular Nonlinear Networks

Information processing in the brain takes place in a dense network of neurons connected through synapses. The collaborative work between these two components (Synapses and Neurons) allows for basic brain functions such as learning and memorization. The so-called von Neumann bottleneck, which limits the information processing capability of conventional systems, can be overcome by the efficient emulation of these computational concepts. To this end, mimicking the neuronal architectures with silicon-based circuits, on which neuromorphic engineering is based, is accompanied by the development of new devices with neuromorphic functionalities. We shall study different memristor cellular nonlinear networks models. The rigorous mathematical analysis will be presented based on local activity theory, and the edge of chaos domain will be determined in the models under consideration. Simulations of these models working on the edge of chaos will show the generation of static and dynamic patterns.

Neuromorphic Dynamics of Chua Corsage Memristor

Neuromorphic computing can solve computationally hard problems with energy efficiencies unattainable for von Neumann architectures. A locally-active memristor, which possesses the capability to amplify infinitesimal fluctuations in energy and can be used to generate neuromorphic behaviors, is a natural candidate for constructing an electronic equivalent of biological neurons. This paper identifies some unknown neuromorphic dynamics of the Chua corsage memristor (CCM), and shows that the CCM, when biased at the edge of chaos domain, can exhibit rich dynamics of biological neurons. Using Chua’s theories of local activity and edge of chaos, we demonstrate that under the destabilizing of the input voltage and the circuit parameters (inductance or capacitance), two CCM-based circuits can produce thirteen types of neuromorphic behaviors either on, or near the edge of chaos domain via supercritical or subcritical Hopf bifurcation. In addition, we give the conditions to test the edge of chaos of the CCM and the CCM-based circuit only by using the poles and the zero of their admittance functions.

Chua Corsage memristor based neuron models

Nowadays, processing of data via neuromorphic non-linear dynamics is a key element for brain-inspired computers. In particular, an appropriate neuromorphic device is essential to emulate neuromorphic functions. In this brief, it is found that the Chua Corsage memristor has rich neuromorphic behaviours, which has potential values to realise the hardware construction for neuromorphic computing. The theory of local activity and edge of chaos are applied to analyse the neuromorphic dynamics of the second-order Chua Corsage memristor based neuron model, and find that the periodic spikes (action potentials) appear either on or near the edge of chaos domain, which are excited by the subcritical Hopf bifurcation or the unstable state of the neuron model, respectively. Furthermore, the third-order Chua Corsage memristor based neuron model can generate self-sustained oscillations, periodic spikes, and chaos near the edge of chaos domain.

Hearts are Poised Near the Edge of Chaos

The Cardiac Purkinje Fiber (CPF) is the last branch of the heart conduction system, which is meshed with the normal ventricular myocyte. Purkinje fiber plays a key role in the occurrence of ventricular arrhythmia and maintenance. Does the heart Purkinje fiber cells have the same memory function as the cerebral nerve? In this paper, the cardiac Hodgkin–Huxley equation is taken as the object of study. In particular, we find that the potassium ion-channel [Formula: see text] and the sodium ion-channel [Formula: see text] are memristors. We also derive the small-signal equivalent circuits about the equilibrium points of the CPF Hodgkin–Huxley model. According to the principle of local activity, the regions of Locally-Active domain, Edge of Chaos domain and Locally-Passive domain are partitioned under parameters [Formula: see text], and the domain exhibiting the normal human heartbeat frequency range (Goldilocks Zone) is identified. Meanwhile, the Super-Critical Hopf bifurcation of the CPF Hodgkin–Huxley model is identified. Finally, the migration changes between different state domains under external current [Formula: see text] excitation are analyzed in detail. All of the above complex nonlinear dynamics are distilled and mapped geometrically into a surreal union of intersecting two-dimensional manifolds, dubbed the Hodgkin–Huxley’s magic roof.

Application of Local Activity Theory of Cellular Neural Network with Two Ports to the Coupled Lorenz-Cell Model**The project supported by National Natural Science Foundation of China under Grant No. 60074034 and the Foundation for University Key Teacher by the Ministry of Education of China

Some criteria for the local activity theory in two-port cellular neural network cells with three local state variables are applied to a coupled Lorenz-cell model. The numerical simulation exhibited that emergence may exist if the selected cell parameters are nearby or on the edge of chaos domain. The local activity theory has provided a new tool of studying the complexity of high dimensional coupled nonlinear physical systems.