A New Locally Active Memristive Synapse Coupled Neuron Model

Abstract In this paper, a new type of non-volatile locally active memristor with bi-stability is proposed by injecting appropriate voltage pulses to realize a switching mechanism between two stable states. It is found that the memristive parameters of the new memristor can affect the local activity, which has been rarely reported, and this phenomenon is explained based on mathematical analyses and numerical simulations. Then, a locally active memristive coupled neuron model is constructed using the proposed memristor as a connecting synapse. The parameter-associated dynamical behaviors are revealed by bifurcation plots, phase plane portraits and dynamical evolution maps. Moreover, the bi-stability phenomenon of the new coupled neuron model is disclosed by local attraction basins, and the periodic burster and multi-scroll chaotic burster are found if a multi-level pulse current is used to imitate a periodical external stimulus on the neurons. The Hamiltonian energy function is calculated and analyzed with or without external excitation. Finally, the neuronal circuit is designed and implemented, which can mimic electrical activity of the neurons and is useful for physical applications. The experimental results captured from the analog circuit are consistent well with the numerical simulation results.

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Riddled Attraction Basin and Multistability in Three-Element-Based Memristive Circuit

Complexity ◽

10.1155/2020/4624792 ◽

2020 ◽

Vol 2020 ◽

pp. 1-13

Author(s):

Quan Xu ◽

Xiao Tan ◽

Yunzhen Zhang ◽

Han Bao ◽

Yihua Hu ◽

...

Keyword(s):

Limit Cycles ◽

Phase Plane ◽

Initial Conditions ◽

Equilibrium Points ◽

Model Parameters ◽

Stable Node ◽

Dynamical Behaviors ◽

Attraction Basins ◽

Memristive Circuit ◽

Crisis Scenarios

By coupling a diode bridge-based second-order memristor and an active voltage-controlled memristor with a capacitor, a three-element-based memristive circuit is synthesized and its system model is then built. The boundedness of the three-element-based memristive circuit is theoretically proved by employing the contraction mapping principle. Besides, the stability distributions of equilibrium points are theoretically and numerically expounded in a 2D parameter plane. The results imply the memristive circuit has a zero unstable saddle focus and a pair of nonzero stable node-foci or unstable saddle-foci depending on the considered parameters. The dynamical behaviors include point attractor, period, chaos, coexisting bifurcation mode, period-doubling bifurcation route, and crisis scenarios, which are explored using some common dynamical methods. Of particular concern, riddled attraction basins and multistability are uncovered under two sets of specified model parameters nearing the tiny neighborhood of crisis scenarios by local attraction basins and phase plane plots. The riddled attraction basins with island-like structure demonstrate that their dynamical behaviors are extremely sensitive to the initial conditions, resulting in the coexistence of limit cycles with period-2 and period-6, as well as the coexistence of period-1 limit cycles and single-scroll chaotic attractors. Moreover, a feasible on-breadboard hardware circuit is manually made and the experimental measurements are executed, upon which phase plane trajectories for some discrete model parameters are captured to further confirm the numerically simulated ones.

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A Simple Nonautonomous Hidden Chaotic System with a Switchable Stable Node-Focus

International Journal of Bifurcation and Chaos ◽

10.1142/s0218127419501682 ◽

2019 ◽

Vol 29 (12) ◽

pp. 1950168 ◽

Cited By ~ 5

Author(s):

Bocheng Bao ◽

Jiaoyan Luo ◽

Han Bao ◽

Chengjie Chen ◽

Huagan Wu ◽

...

Keyword(s):

Phase Plane ◽

Value Function ◽

Analog Circuit ◽

Nonautonomous System ◽

Stable Node ◽

Two Dimensional ◽

Coexisting Attractors ◽

Absolute Value ◽

Dynamical Behaviors ◽

Hidden Oscillations

This paper presents a simple two-dimensional nonautonomous system, which possesses piecewise linearity constructed by a simple absolute value function. The nonautonomous system has only one switchable equilibrium state with a stable node-focus in the considered control parameter region but can generate periodic, chaotic and coexisting attractors. Therefore, the presented simple two-dimensional nonautonomous system always operates with hidden oscillations, which is not similar to any example reported in the literature. Furthermore, specific hidden dynamical behaviors are numerically disclosed by employing one-dimensional and two-dimensional bifurcation plots, phase plane plots, Poincaré mappings, local attraction basins, and complexity plots. In addition, by utilizing the circuit module of the absolute value function, a multiplierless analog circuit is designed, based on which breadboard experiments are performed to validate the numerically simulated phase plane plots of coexisting attractors.

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Chaotic Bursting Dynamics and Coexisting Multistable Firing Patterns in 3D Autonomous Morris–Lecar Model and Microcontroller-Based Validations

International Journal of Bifurcation and Chaos ◽

10.1142/s0218127419501347 ◽

2019 ◽

Vol 29 (10) ◽

pp. 1950134 ◽

Cited By ~ 11

Author(s):

Bocheng Bao ◽

Qinfeng Yang ◽

Lei Zhu ◽

Han Bao ◽

Quan Xu ◽

...

Keyword(s):

Neuron Model ◽

Phase Plane ◽

Three Dimensional ◽

Model Parameters ◽

Fast Subsystem ◽

Firing Patterns ◽

Chaotic Bursting ◽

Attraction Basins ◽

Initial States ◽

Electronic Neuron

A three-dimensional (3D) autonomous Morris–Lecar (simplified as M–L) neuron model with fast and slow structures was proposed to generate periodic bursting behaviors. However, chaotic bursting dynamics and coexisting multistable firing patterns have been rarely discussed in such a 3D M–L neuron model. For some specified model parameters, MATLAB numerical plots are executed by bifurcation plots, time sequences, phase plane plots, and 0–1 tests, from which diverse forms of chaotic bursting, chaotic tonic-spiking, and periodic bursting behaviors are uncovered in the 3D M–L neuron model. Furthermore, based on the theoretically constructing fold/Hopf bifurcation sets of the fast subsystem, the bifurcation mechanism for the chaotic bursting behaviors is thereby expounded qualitatively. Particularly, through numerically plotting the attraction basins related to the initial states under two sets of specific parameters, coexisting multistable firing patterns are demonstrated in the 3D M–L neuron model also. Finally, a digitally circuit-implemented electronic neuron is generated based on a low-power microcontroller and its experimentally captured results faultlessly validate the numerical plots.

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Hidden dynamical behaviors, sliding mode control and circuit implementation of fractional-order memristive Hindmarsh−Rose neuron model

The European Physical Journal Plus ◽

10.1140/epjp/s13360-021-01107-6 ◽

2021 ◽

Vol 136 (5) ◽

Author(s):

Dawei Ding ◽

Li Jiang ◽

Yongbing Hu ◽

Qian Li ◽

Zongli Yang ◽

...

Keyword(s):

Sliding Mode Control ◽

Fractional Order ◽

Neuron Model ◽

Sliding Mode ◽

Circuit Implementation ◽

Mode Control ◽

Dynamical Behaviors

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Quaternion quantum neurocomputing

International Journal of Wavelets Multiresolution and Information Processing ◽

10.1142/s0219691320400019 ◽

2020 ◽

pp. 2040001

Author(s):

Eduardo Bayro-Corrochano ◽

Samuel Solis-Gamboa

Keyword(s):

Neural Network ◽

Geometric Algebra ◽

Neuron Model ◽

Quaternion Algebra ◽

Quantum States ◽

Robust Performance ◽

Quantum Neural Network ◽

Quantum Operator ◽

New Type

Since the introduction of quaternion by Hamilton in 1843, quaternions have been used in a lot of applications. One of the most interesting qualities is that we can use quaternions to carry out rotations and operate on other quaternions; this characteristic of the quaternions inspired us to investigate how the quantum states and quantum operator work in the field of quaternions and how we can use it to construct a quantum neural network. This new type of quantum neural network (QNN) is developed in the quaternion algebra framework that is isomorphic to the rotor algebra [Formula: see text] of the geometric algebra and is based on the so-called qubit neuron model. The quaternion quantum neural network (QQNN) is tested and shows robust performance.

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EFFECT OF TIME-DELAY ON A PREY–PREDATOR MODEL WITH MICROPARASITE INFECTION IN THE PREDATOR

Journal of Biological System ◽

10.1142/s0218339011004032 ◽

2011 ◽

Vol 19 (02) ◽

pp. 365-387 ◽

Cited By ~ 4

Author(s):

SWETA PATHAK ◽

ALAKES MAITI ◽

SHYAM PADA BERA

Keyword(s):

Time Delay ◽

Discrete Time ◽

Predator Population ◽

Dynamical Characteristics ◽

Dynamical Behaviors ◽

Discrete Time Delay ◽

Mathematical Analyses ◽

Predator Model ◽

Living Organisms

To increase a prey population that is attacked by a predator it is more convenient and economical to choose the living organisms to control the predator. In this paper, the dynamical behaviors of a prey–predator model with microparasitic infection in the predator have been discussed. In this epidemiological model the microparasite is horizontally transmitted and attacks the predator population only. The infected population does not recover or become immune. The dynamical characteristics of the system are studied through mathematical analyses. The role of discrete time-delay has been discussed to show that time-delay can induce instability and oscillation. Numerical simulations are carried out. Biological implications have been discussed.

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ON THE STRUCTURE OF REAL-VALUED ONE-DIMENSIONAL CELLULAR AUTOMATA

International Journal of Bifurcation and Chaos ◽

10.1142/s0218127411029240 ◽

2011 ◽

Vol 21 (05) ◽

pp. 1265-1279 ◽

Cited By ~ 5

Author(s):

XU XU ◽

STEPHEN P. BANKS ◽

MAHDI MAHFOUF

Keyword(s):

Cellular Automata ◽

Cellular Automaton ◽

Fixed Points ◽

Periodic Solutions ◽

Cellular Systems ◽

One Dimensional ◽

Dynamical Behaviors ◽

New Type ◽

Complex Patterns

It is well-known that binary-valued cellular automata, which are defined by simple local rules, have the amazing feature of generating very complex patterns and having complicated dynamical behaviors. In this paper, we present a new type of cellular automaton based on real-valued states which produce an even greater amount of interesting structures such as fractal, chaotic and hypercyclic. We also give proofs to real-valued cellular systems which have fixed points and periodic solutions.

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Dynamic Modeling and Experimental Verification of A Cable-Driven Continuum Manipulator With Cable-Constrained Synchronous Rotating Mechanisms

10.21203/rs.3.rs-609741/v1 ◽

2021 ◽

Author(s):

Xudong Zheng ◽

Taiwei Yang ◽

Xianjin Zhu ◽

Zhang Chen ◽

Xueqian Wang ◽

...

Keyword(s):

Dynamic Modeling ◽

Friction Model ◽

Modeling Method ◽

Stick Slip ◽

Dynamical Behaviors ◽

Ale Formulation ◽

Two Factors ◽

New Type ◽

Continuum Manipulator ◽

Coulomb Friction Model

Abstract The cable-driven segmented manipulator with cable-constrained synchronous rotating mechanisms (CCSRM) is a new type of continuum manipulator, which has large stiffness and less motors, and thus exhibits excellent comprehensive performance. This paper presents a dynamic modeling method for this type of manipulator to analyze the friction and deformation of the cables on the dynamical behaviors of the system. First, the driving cables are modeled based on the ALE formulation, the strategies for detecting stick-slip transitions are proposed by using a trial-and-error algorithm, and the stiff problems of the dynamic equations are released by a model smoothing method. Second, the dynamic modeling method for rigid links is presented by using quaternion parameters. Third, the connecting cables are modeled by torsional spring-dampers and the frictions between the connecting cables and the conduits are considered based on a modified Coulomb friction model. Finally, the numerical results are presented and verified by comparing with experiment results. The study shows that the friction and cable deformation play an important role in the dynamical behaviors of the manipulator. Due to these two factors, the constant curvature bending of the segments does not remain.

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The vertical distribution of buoyant plastics at sea

Biogeosciences Discussions ◽

10.5194/bgd-11-16207-2014 ◽

2014 ◽

Vol 11 (11) ◽

pp. 16207-16226 ◽

Cited By ~ 16

Author(s):

J. Reisser ◽

B. Slat ◽

K. Noble ◽

K. du Plessis ◽

M. Epp ◽

...

Keyword(s):

Turbulent Transport ◽

Marine Species ◽

Decay Rates ◽

Transport Models ◽

The North ◽

New Type ◽

Multi Level ◽

Load Size ◽

The Vertical Distribution ◽

Numerical Concentration

Abstract. Millimeter-sized plastics are numerically abundant and widespread across the world's ocean surface. These buoyant macroscopic particles can be mixed within the upper water column due to turbulent transport. Models indicate that the largest decrease in their concentration occurs within the first few meters of water, where subsurface observations are very scarce. By using a new type of multi-level trawl at 12 sites within the North Atlantic accumulation zone, we measured concentrations and physical properties of plastics from the air–seawater interface to a depth of 5 m, at 0.5 m intervals. Our results show that plastic concentrations drop exponentially with water depth, but decay rates decrease with increasing Beaufort scale. Furthermore, smaller pieces presented lower rise velocities and were more susceptible to vertical transport. This resulted in higher depth decays of plastic mass concentration (mg m−3) than numerical concentration (pieces m−3). Further multi-level sampling of plastics will improve our ability to predict at-sea plastic load, size distribution, drifting pattern, and impact on marine species and habitats.

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