Dynamic Analysis of a Bistable Bi-Local Active Memristor and Its Associated Oscillator System

2018 ◽  
Vol 28 (08) ◽  
pp. 1850105 ◽  
Author(s):  
Hui Chang ◽  
Zhen Wang ◽  
Yuxia Li ◽  
Guanrong Chen
Keyword(s):  
Hopf Bifurcation ◽  
Bifurcation Theory ◽  
Hysteresis Loops ◽  
Oscillator System ◽  
Local Activity ◽  
Edge Of Chaos ◽  
Bifurcation Phenomenon ◽  
Subcritical Hopf Bifurcation ◽  
New Type ◽  
Pinched Hysteresis

This paper proposes a new type of memristor with two distinct stable pinched hysteresis loops and twin symmetrical local activity domains, named as a bistable bi-local active memristor. A detailed and comprehensive analysis of the memristor and its associated oscillator system is carried out to verify its dynamic behaviors based on nonlinear circuit theory and Hopf bifurcation theory. The local-activity domains and the edge-of-chaos domains of the memristor, which are both symmetric with respect to the origin, are confirmed by utilizing the mathematical cogent theory. Finally, the subcritical Hopf bifurcation phenomenon is identified in the subcritical Hopf bifurcation region of the memristor.

scholarly journals Modelling HIV dynamics with cell-to-cell transmission and CTL response

2021 ◽  
Author(s):  
Zirui Zhu ◽  
Ranchao Wu ◽  
Yu Yang ◽  
Yancong Xu
Keyword(s):  
Hopf Bifurcation ◽  
Cell Interaction ◽  
Backward Bifurcation ◽  
Hiv Treatment ◽  
Hiv Model ◽  
Ctl Response ◽  
Hiv Dynamics ◽  
Subcritical Hopf Bifurcation ◽  
Cell Transmission ◽  
New Type

In most HIV models, the emergence of backward bifurcation means that the control for basic reproduction number less than one is no longer effective for HIV treatment. In this paper, we study an HIV model with CTL response and cell-to-cell transmission by using the dynamical approach. The local and global stability of equilibria is investigated, the relations of subcritical Hopf bifurcation and supercritical bifurcation points are revealed, especially, the so-called new type bifurcation is also found with two Hopf bifurcation curves meeting at the same Bogdanov-Takens bifurcation point. Forward and backward bifurcation, Hopf bifurcation, saddle-node bifurcation, Bogdanov-Takens bifurcation are investigated analytically and numerically. Two limit cycles are also found numerically, which indicates that the complex behavior of HIV dynamics. Interestingly, the role of cell-to-cell interaction is fully uncovered, it may cause the oscillations to disappear and keep the so-called new type bifurcation persist. Finally, some conclusions and discussions are also given.

Chua Corsage Memristor Oscillator via Hopf Bifurcation

2016 ◽  
Vol 26 (04) ◽  
pp. 1630009 ◽  
Author(s):  
Zubaer Ibna Mannan ◽  
Hyuncheol Choi ◽  
Hyongsuk Kim
Keyword(s):  
Hopf Bifurcation ◽  
Equivalent Circuit ◽  
Series Expansion ◽  
Taylor Series ◽  
Taylor Series Expansion ◽  
Operating Point ◽  
Small Signal ◽  
Local Activity ◽  
Edge Of Chaos ◽  
In Series

This paper demonstrates that the Chua Corsage Memristor, when connected in series with an inductor and a battery, oscillates about a locally-active operating point located on the memristor’s DC [Formula: see text]–[Formula: see text] curve. On the operating point, a small-signal equivalent circuit is derived via a Taylor series expansion. The small-signal admittance [Formula: see text] is derived from the small-signal equivalent circuit and the value of inductance is determined at a frequency where the real part of the admittance [Formula: see text] of the small-signal equivalent circuit of Chua Corsage Memristor is zero. Oscillation of the circuit is analyzed via an in-depth application of the theory of Local Activity, Edge of Chaos and the Hopf-bifurcation.

NEURONS ARE POISED NEAR THE EDGE OF CHAOS

2012 ◽  
Vol 22 (04) ◽  
pp. 1250098 ◽  
Author(s):  
LEON CHUA ◽  
VALERY SBITNEV ◽  
HYONGSUK KIM
Keyword(s):  
Hopf Bifurcation ◽  
Bifurcation Point ◽  
Nonlinear Differential Equations ◽  
Complex Conjugate ◽  
Excitation Current ◽  
Hopf Bifurcation Point ◽  
Synaptic Excitation ◽  
Edge Of Chaos ◽  
Subcritical Hopf Bifurcation ◽  
Dc Current

This paper shows the action potential (spikes) generated from the Hodgkin–Huxley equations emerges near the edge of chaos consisting of a tiny subset of the locally active regime of the HH equations. The main result proves that the eigenvalues of the 4 × 4 Jacobian matrix associated with the mathematically intractable system of four nonlinear differential equations are identical to the zeros of a scalar complexity function from complexity theory. Moreover, we show the loci of a pair of complex-conjugate zeros migrate continuously as a function of an externally applied DC current excitation emulating the net synaptic excitation current input to the neuron. In particular, the pair of complex-conjugate zeros move from a subcritical Hopf bifurcation point at low excitation current to a super-critical Hopf bifurcation point at high excitation current. The spikes are generated as the excitation current approaches the vicinity of the edge of chaos, which leads to the onset of the subcritical Hopf bifurcation regime. It follows from this in-depth qualitative analysis that local activity is the origin of spikes.

Oscillator Made of Only One Memristor and One Battery

2015 ◽  
Vol 25 (03) ◽  
pp. 1530010 ◽  
Author(s):  
Maheshwar PD. Sah ◽  
Zubaer Ibna Mannan ◽  
Hyongsuk Kim ◽  
Leon Chua
Keyword(s):  
Energy Storage ◽  
Hopf Bifurcation ◽  
Intimate Relationship ◽  
Edge Of Chaos ◽  
Traditional Belief ◽  
Bifurcation Phenomenon ◽  
Circuit Elements ◽  
Electronic Oscillator

Contrary to the traditional belief that at least two energy-storage elements (capacitor and/or inductor) and a locally-active nonlinearity are needed to build an electronic oscillator, this paper presents an oscillator made with only two circuit elements, namely, a memristor and a battery. This simplest of all physical oscillators also serves as a textbook example for explaining the intimate relationship between the super-critical Hopf bifurcation phenomenon and the edge of chaos.

scholarly journals Unstable Limit Cycles and Singular Attractors in a Two-Dimensional Memristor-Based Dynamic System

Entropy ◽  
2019 ◽  
Vol 21 (4) ◽  
pp. 415 ◽  
Author(s):  
Hui Chang ◽  
Qinghai Song ◽  
Yuxia Li ◽  
Zhen Wang ◽  
Guanrong Chen
Keyword(s):  
Hopf Bifurcation ◽  
Dynamic System ◽  
Numerical Simulations ◽  
Limit Cycles ◽  
Two Dimensional ◽  
Local Activity ◽  
Period 2 ◽  
Subcritical Hopf Bifurcation ◽  
Dimensional Dynamical System ◽  
Nested Intervals

This paper reports the finding of unstable limit cycles and singular attractors in a two-dimensional dynamical system consisting of an inductor and a bistable bi-local active memristor. Inspired by the idea of nested intervals theorem, a new programmable scheme for finding unstable limit cycles is proposed, and its feasibility is verified by numerical simulations. The unstable limit cycles and their evolution laws in the memristor-based dynamic system are found from two subcritical Hopf bifurcation domains, which are subdomains of twin local activity domains of the memristor. Coexisting singular attractors are discovered in the twin local activity domains, apart from the two corresponding subcritical Hopf bifurcation domains. Of particular interest is the coexistence of a singular attractor and a period-2 or period-3 attractor, observed in numerical simulations.

Subcritical Hopf bifurcation in NeNd hollow cathode discharge

1994 ◽  
Vol 196 (3-4) ◽  
pp. 191-194 ◽  
Author(s):  
P.R. Sasi Kumar ◽  
V.P.N. Nampoori ◽  
C.P.G. Vallabhan
Keyword(s):  
Hopf Bifurcation ◽  
Hollow Cathode ◽  
Hollow Cathode Discharge ◽  
Subcritical Hopf Bifurcation

Nonlinear Vibration Analysis of a Flexible Rotor Supported by a Flexure Pivot Tilting Pad Journal Bearing in Comparison to a Fixed Profile Journal Bearing with Experimental Verification

2021 ◽  
Author(s):  
Nuntaphong Koondilogpiboon ◽  
Tsuyoshi Inoue
Keyword(s):  
Hopf Bifurcation ◽  
Journal Bearing ◽  
Flexible Rotor ◽  
Maximum Test ◽  
Operating Region ◽  
Stable Operating ◽  
Subcritical Hopf Bifurcation ◽  
Tilting Pad ◽  
Calculation Results ◽  
Tilting Pad Journal Bearing

Abstract In this paper, an efficient numerical method consisting of the real mode component mode synthesis (CMS) model reduction, shooting method with parallel computing, and Floquet analysis was developed for nonlinear rotordynamics analysis of a flexible rotor supported by a 4-lobe flexure pivot tilting pad journal bearing (FPTPJB) in load-on-pad (LOP) and load-between-pad (LBP) orientations in comparison to a fixed profile journal bearing (JB) of the same pad geometry. The method used the rotor's finite elements and bearing forces obtained from directly solving the Reynolds equation to determine the limit cycles and Hopf bifurcation types. For the investigated rotor and bearing parameters, the numerical results indicated that the onset speed of instability (OSI) of FPTPJB is considerably higher than that of JB of the same orientation. Also, FPTPJB in LOP orientation yielded higher OSI than the LBP one, whereas the OSI of JB in LOP orientation was substantially higher than the LBP counterpart. Nonlinear calculation results indicated that all bearing types and orientations gave subcritical Hopf bifurcation. The FPTPJB in LOP orientation produced the largest stable operating region, whereas the JB in LBP configuration yield the smallest one. The experiment showed subcritical Hopf bifurcation occurred at speed close to the calculated OSI in all cases except FPTPJB in LOP orientation that the OSI is higher than the maximum test rig speed. The whirling orbit had the same frequency as the first critical speed and precessed in the direction of shaft rotation.

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