scholarly journals A Nonvolatile Fractional Order Memristor Model and its Complex Dynamics

Entropy ◽  
2019 ◽  
Vol 21 (10) ◽  
pp. 955 ◽  
Author(s):  
Wu ◽  
Wang ◽  
Iu ◽  
Shen ◽  
Zhou
Keyword(s):  
Fractional Order ◽  
Complex Dynamics ◽  
Equilibrium Points ◽  
Stable State ◽  
Electrical Characteristics ◽  
Chaotic Circuit ◽  
Stable States ◽  
Road Map ◽  
Chaotic Circuits ◽  
Integral Order

It is found that the fractional order memristor model can better simulate the characteristics of memristors and that chaotic circuits based on fractional order memristors also exhibit abundant dynamic behavior. This paper proposes an active fractional order memristor model and analyzes the electrical characteristics of the memristor via Power-Off Plot and Dynamic Road Map. We find that the fractional order memristor has continually stable states and is therefore nonvolatile. We also show that the memristor can be switched from one stable state to another under the excitation of appropriate voltage pulse. The volt–ampere hysteretic curves, frequency characteristics, and active characteristics of integral order and fractional order memristors are compared and analyzed. Based on the fractional order memristor and fractional order capacitor and inductor, we construct a chaotic circuit, of which the dynamic characteristics with respect to memristor’s parameters, fractional order α, and initial values are analyzed. The chaotic circuit has an infinite number of equilibrium points with multi-stability and exhibits coexisting bifurcations and coexisting attractors. Finally, the fractional order memristor-based chaotic circuit is verified by circuit simulations and DSP experiments.

scholarly journals Dynamic Analysis and Circuit Design of a Novel Hyperchaotic System with Fractional-Order Terms

Complexity ◽  
2017 ◽  
Vol 2017 ◽  
pp. 1-10 ◽  
Author(s):  
Abir Lassoued ◽  
Olfa Boubaker
Keyword(s):  
Dynamic Analysis ◽  
Circuit Design ◽  
Fractional Order ◽  
Potential Application ◽  
Complex Dynamics ◽  
Equilibrium Points ◽  
Hyperchaotic System ◽  
Software Simulation ◽  
Simulation Results ◽  
Hyperchaotic Systems

A novel hyperchaotic system with fractional-order (FO) terms is designed. Its highly complex dynamics are investigated in terms of equilibrium points, Lyapunov spectrum, and attractor forms. It will be shown that the proposed system exhibits larger Lyapunov exponents than related hyperchaotic systems. Finally, to enhance its potential application, a related circuit is designed by using the MultiSIM Software. Simulation results verify the effectiveness of the suggested circuit.

Dynamical analysis of fractional-order differentiated Cournot triopoly game

2020 ◽  
Vol 26 (15-16) ◽  
pp. 1367-1380
Author(s):  
Abdulrahman Al-khedhairi
Keyword(s):  
Stability Analysis ◽  
Fractional Order ◽  
Complex Dynamics ◽  
Equilibrium Points ◽  
Sufficient Conditions ◽  
Dynamical Analysis ◽  
Periodic Forcing ◽  
Nash Equilibrium Point ◽  
Dynamical Behaviors ◽  
Theoretical Results

The objective of the article is to study the dynamics of the proposed fractional-order Cournot triopoly game. Sufficient conditions for the existence and uniqueness of the triopoly game solution are obtained. Stability analysis of equilibrium points of the fractional-order game is also discussed. The conditions for the presence of Nash equilibrium point along with its global stability analysis are studied. The interesting dynamical behaviors of the arbitrary-order Cournot triopoly game are discussed. Moreover, the effects of seasonal periodic forcing on the game’s behaviors are examined. The 0–1 test is used to distinguish between regular and irregular dynamics of system behaviors. Numerical analysis is used to verify the theoretical results that are obtained, and revealed that the nonautonomous fractional-order model induces more complicated dynamics in the Cournot triopoly game behavior and the seasonally forced game exhibits more complex dynamics than the unforced one.

Switching Characteristics of a Locally-Active Memristor with Binary Memories

2019 ◽  
Vol 29 (11) ◽  
pp. 1930030 ◽  
Author(s):  
Jiajie Ying ◽  
Guangyi Wang ◽  
Yujiao Dong ◽  
Simin Yu
Keyword(s):  
Voltage Pulse ◽  
Pulse Width ◽  
Pulse Sequence ◽  
Equilibrium Points ◽  
Stable State ◽  
Active Regions ◽  
Pulse Amplitude ◽  
Chaotic Oscillator ◽  
Stable States ◽  
Local Activity

A number of important applications would benefit from the introduction of locally-active memristors, which is defined to be any memristor that exhibits negative differential memristance for at least a voltage or a current applied to the memristor. Two leading examples are emerging nonvolatile memory based on memristor-based crossbar array architectures, and neural networks that exhibit improved computational complexity when operated at the edge of chaos. In this paper, a novel locally-active memristor model is presented for exploring the nonvolatile and switching mechanism of the memristor and the influence of local activity on the complexity of nonlinear circuits. We find that the memristor possesses three locally-active regions in its DC [Formula: see text]–[Formula: see text] plot and two asymptotically stable states (equilibrium points) on its power-off plot (POP) where voltage [Formula: see text], implying that the memristor is bistable, which can be used as a nonvolatile binary memory or binary switch. We also find the mechanism and the rule of switching between the two stable states by applying a single square voltage pulse of appropriate pulse width and pulse amplitude. We show that it is always possible to switch from one stable state to another of the memristor with an appropriate pulse amplitude and a pulse width, and that there is a trade-off between the voltage pulse amplitude and the pulse width for the faster switching between the two equilibrium points. We also show that fast switching between the two states is possible by using a periodic bipolar narrow pulse sequence. Local activity depends on the capability of a memristor circuit to amplify infinitesimal fluctuations in energy. Based on this principle, we designed a simplest chaotic oscillator that utilizes only three components in parallel: the proposed locally-active memristor, a linear capacitor and an inductor, which can oscillate around an equilibrium point located on its DC [Formula: see text]–[Formula: see text] plot. Its dynamic characteristics are verified by theoretical analyses, simulations and DSP experiments.

scholarly journals Dynamic Behaviors and the Equivalent Realization of a Novel Fractional-Order Memristor-Based Chaotic Circuit

Complexity ◽  
2018 ◽  
Vol 2018 ◽  
pp. 1-13 ◽  
Author(s):  
Ningning Yang ◽  
Cheng Xu ◽  
Chaojun Wu ◽  
Rong Jia ◽  
Chongxin Liu
Keyword(s):  
Numerical Simulations ◽  
Dynamic Behavior ◽  
Fractional Order ◽  
Equilibrium Points ◽  
Dynamical Behavior ◽  
Great Influence ◽  
Equivalent Circuits ◽  
Chaotic Circuit ◽  
Undetermined Coefficient ◽  
The Stability

This paper proposed a novel fractional-order memristor-based chaotic circuit. A memristive diode bridge cascaded with a fractional-order RL filter constitutes the generalized fractional-order memristor. The mathematical model of the proposed fractional-order chaotic circuit is established by extending the nonlinear capacitor and inductor in the memristive chaotic circuit to the fractional order. Detailed theoretical analysis and numerical simulations are carried out on the dynamic behavior of the proposed circuit by investigating the stability of equilibrium points and the influence of circuit parameters on bifurcations. The results show that the order of the fractional-order circuit has a great influence on the dynamical behavior of the system. The system may exhibit complicated nonlinear dynamic behavior such as bifurcation and chaos with the change of the order. The equivalent circuits of the fractional-order inductor and capacitor are also given in the paper, and the parameters of the equivalent circuits are solved by an undetermined coefficient method. Circuit simulations of the equivalent fractional-order memristive chaotic circuit are carried out in order to validate the correctness of numerical simulations and the practicability of using the integer-order equivalent circuit to substitute the fractional-order element.

scholarly journals Path-dependent institutions drive alternative stable states in conservation

2018 ◽  
Vol 116 (2) ◽  
pp. 689-694 ◽  
Author(s):  
Edward W. Tekwa ◽  
Eli P. Fenichel ◽  
Simon A. Levin ◽  
Malin L. Pinsky
Keyword(s):  
Renewable Resources ◽  
Path Dependence ◽  
Alternative Stable States ◽  
Stable State ◽  
Empirical Support ◽  
Stable States ◽  
Alternative Stable State ◽  
Important Challenge ◽  
Quantitative Analyses ◽  
Path Dependent

Understanding why some renewable resources are overharvested while others are conserved remains an important challenge. Most explanations focus on institutional or ecological differences among resources. Here, we provide theoretical and empirical evidence that conservation and overharvest can be alternative stable states within the same exclusive-resource management system because of path-dependent processes, including slow institutional adaptation. Surprisingly, this theory predicts that the alternative states of strong conservation or overharvest are most likely for resources that were previously thought to be easily conserved under optimal management or even open access. Quantitative analyses of harvest rates from 217 intensely managed fisheries supports the predictions. Fisheries’ harvest rates also showed transient dynamics characteristic of path dependence, as well as convergence to the alternative stable state after unexpected transitions. This statistical evidence for path dependence differs from previous empirical support that was based largely on case studies, experiments, and distributional analyses. Alternative stable states in conservation appear likely outcomes for many cooperatively managed renewable resources, which implies that achieving conservation outcomes hinges on harnessing existing policy tools to navigate transitions.

scholarly journals Developing the Concepts of Homeostasis, Homeorhesis, Allostasis, Elasticity, Flexibility and Plasticity of Brain Function

NeuroSci ◽  
2021 ◽  
Vol 2 (4) ◽  
pp. 372-382
Author(s):  
Alfredo Pereira
Keyword(s):  
Brain Function ◽  
Complex Dynamics ◽  
Stable States ◽  
Set Point ◽  
Brain Functions ◽  
Temporal Phase ◽  
The Central Nervous System ◽  
Elastic Processes ◽  
And Control ◽  
Flexible Processes

I discuss some concepts advanced for the understanding of the complex dynamics of brain functions, and relate them to approaches in affective, cognitive and action neurosciences. These functions involve neuro-glial interactions in a dynamic system that receives sensory signals from the outside of the central nervous system, processes information in frequency, amplitude and phase-modulated electrochemical waves, and control muscles and glands to generate behavioral patterns. The astrocyte network is in charge of controlling global electrochemical homeostasis, and Hodgkin–Huxley dynamics drive the bioelectric homeostasis of single neurons. In elastic processes, perturbations cause instability, but the system returns to the basal equilibrium. In allostatic processes, perturbations elicit a response from the system, reacting to the deviation and driving the system to stable states far from the homeostatic equilibrium. When the system does not return to a fixed point or region of the state space, the process is called homeorhetic, and may present two types of evolution: (a) In flexible processes, there are previously existing “attractor” stable states that may be achieved after the perturbation, depending on context; (b) In plastic processes, the homeostatic set point(s) is(are) changed; the system is in a process of adaptation, in which the allostatic forces do not drive it back to the previous set point, but project to the new one. In the temporal phase from the deviant state to the recovery of stability, the system generates sensations that indicate if the recovery is successful (pleasure-like sensations) or if there is a failure (pain-like sensations).

scholarly journals Complex dynamics of a fractional-order SIR system in the context of COVID-19

2022 ◽  
Author(s):  
Suvankar Majee ◽  
Sayani Adak ◽  
Soovoojeet Jana ◽  
Manotosh Mandal ◽  
T. K. Kar
Keyword(s):  
Fractional Order ◽  
Complex Dynamics

scholarly journals Theory and applications of new fractional-order chaotic system under Caputo operator

2021 ◽  
Vol 12 (1) ◽  
pp. 20-38
Author(s):  
Ndolane Sene
Keyword(s):  
Fractional Order ◽  
Chaotic System ◽  
Caputo Derivative ◽  
Phase Portraits ◽  
Chaotic Circuit ◽  
Chaotic Model ◽  
The Stability ◽  
The Impact ◽  
Schematic Circuit ◽  
Good Agreement

This paper introduces the properties of a fractional-order chaotic system described by the Caputo derivative. The impact of the fractional-order derivative has been focused on. The phase portraits in different orders are obtained with the aids of the proposed numerical discretization, including the discretization of the Riemann-Liouville fractional integral. The stability analysis has been used to help us to delimit the chaotic region. In other words, the region where the order of the Caputo derivative involves and where the presented system in this paper is chaotic. The nature of the chaos has been established using the Lyapunov exponents in the fractional context. The schematic circuit of the proposed fractional-order chaotic system has been presented and simulated in via Mutltisim. The results obtained via Multisim simulation of the chaotic circuit are in good agreement with the results with Matlab simulations. That provided the fractional operators can be applied in real- worlds applications as modeling electrical circuits. The presence of coexisting attractors for particular values of the parameters of the presented fractional-order chaotic model has been studied.

Design and Characterization of Single Beam for Latching Electrothermal Microswitch

2012 ◽  
Vol 468-471 ◽  
pp. 286-289
Author(s):  
Ying Zhang ◽  
Hong Wang ◽  
Yan Wang ◽  
Sheng Ping Mao ◽  
Gui Fu Ding
Keyword(s):  
Mechanical Performance ◽  
Stable State ◽  
Cantilever Beams ◽  
Analysis Software ◽  
Stable States ◽  
Element Analysis ◽  
Single Beam ◽  
Fabrication And Characterization ◽  
Continuous Power

This paper presents the design, fabrication and characterization of single beam for latching electrothermal microswitch. This microswitch consists of two cantilever beams using bimorph electrothermal actuator with mechanical latching for performing low power bistable relay applications. A stable state can be acquired without continuous power which is only needed to switch between two stable states of the microactuator. The single beam is discussed mainly to judge the possibility of realizing the designed function. First, reasonable shape of the resistance is designed using finite element analysis software ANSYS. Then, mechanical performance was characterized by WYKO NT1100 optical profiling system, the tip deflection of single beam can meet the designed demand.

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