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In this paper, we present a novel two-dimensional discrete memristor map that is based on a discrete memristor model and a sine–arcsine one-dimensional map. First, an analysis is conducted on the memristor model to understand its characteristics. Then, the model is coupled with the sine–arcsine one-dimensional map to achieve the two-dimensional discrete memristor map. Our investigation reveals the presence of coexisting attractors and hyperchaotic attractors as the bifurcation parameters vary. Numerical simulations show that the discrete memristors effectively enhance the complexity of chaos in the sine–arcsine map. Furthermore, a digital circuit is designed to experimentally verify the new chaotic system. The research results can enrich the theoretical analysis and circuit implementation of chaos. [ABSTRACT FROM AUTHOR]

One of the promising applications of locally-active memristors (LAMs) is to construct oscillators for oscillatory neural networks. By using two current-controlled (CC) LAMs, a fully CC LAM-based oscillator is designed in this paper. The oscillator principle originates from the small-signal inductive and capacitive impedance characteristics of two different CC LAMs, and thus extra reactance element is not required in the circuit. Based on bifurcation theory and small-signal analysis method, conditions of the equilibrium point instability are quantitatively derived. Theoretical analysis indicates that the circuit oscillation is dependent on three critical parameters. Then, according to the conditions of the equilibrium point instability, parameters design methods of the two LAMs are proposed, including the static and dynamic parameters. A simple NbOx CC LAM model is taken as an example to conduct detailed simulation analysis. The simulation results verify the feasibility of the proposed circuit and analysis methods. Finally, the effects of the LAM model parameters on the oscillator performance are investigated, which is helpful for optimal design of the oscillator. [ABSTRACT FROM AUTHOR]

Gas detection plays different roles in different environments. Traditional algorithms implemented on electronic nose for gas detection and recognition have high complexity and cannot resist device drift. In response to the above issues, we propose a convolutional neural network based on memristive Stochastic Computing (SC), which combines the characteristics of small devices and low power consumption of memristor devices, as well as the fast and fault-tolerant random calculation speed. It can effectively utilize hardware advantages, recognizing gases by electronic nose. The experimental results show that for two different gas sensor array datasets, the accuracy of the proposed method can achieve the level of 99%. When using memristive SC for deduction, the accuracy decreases by less than 1%, but in drift data, the accuracy can be improved by about 3%. Finally, the improvement in area, power, and energy compared to inference in GPU (NVIDIA Geforce RTX 3060 Laptop) is 1104X, 48X, and 9X, respectively. [ABSTRACT FROM AUTHOR]

Unlike the high-dimensional hyperchaotic system based on a continuous memristor, the low-dimensional map coupled by discrete memristor (DM) and traditional chaotic map can also generate hyperchaos. However, the hyperchaotic map constructed by two DMs has not attracted much attention. To this end, a generalized two-dimensional dual DM-coupled hyperchaotic mapping model is reported in this paper, and four specific maps are provided. The proposed maps have line invariant points, which can be interpreted as allowing arbitrary real values for the initial condition associated with the DM, and the stability is investigated in detail. Furthermore, the coupling strength-dependent and initial condition-dependent complex dynamics of four maps are studied by numerical simulations, and the dynamical performance is evaluated from the perspective of quantitative analysis. It is shown that the considered maps are capable of exhibiting the three characteristic fingerprints of memristors in arbitrary parameter spaces, and this characteristic has gained attention for the first time. In particular, the complete control of the considered maps by variable substitution is performed, which can generate arbitrary switched hyperchaotic behaviors. In addition, four pseudo-random number generators are designed based on the proposed maps, and the randomness is tested by using the NIST SP800-22 software. In general, the proposed maps can not only generate abundant dynamical behaviors, but also enrich the DM circuits and provide a reference for applications based on chaos. Finally, the developed digital hardware circuit implementation platform verifies the results of the numerical method. [ABSTRACT FROM AUTHOR]

In this paper, a type of modified dual memristive Shinriki oscillator is constructed with a flux-controlled absolute-type memristor and a voltage-controlled generic memristor, and the proposed oscillator with abundant dynamical behaviors, including the multistability and antimonotonicity, is comprehensively studied through dynamical distribution graphs, bifurcation diagrams, Lyapunov exponents and phase portraits. It is found that the passive/active state of memristor, which means different characteristics in the v – i domain with positive and negative parameters of the elements, can affect the state of the oscillator. For example, if the memristor is active, the oscillator will change more frequently in the multistable region. Also, it is noted that, for inherent initial-related symmetry and circuit structures with duality, both phenomena have strong symmetric characteristics and opposite evolution trends modulated by values of corresponding components. Especially, the bubbles, which are symmetric about parameters with duality and own complex evolution laws, have rarely been explored in previous works. In addition, the memristive oscillator is modularized based on field programmable gate array (FPGA) technology, and the multiple coexisting attractors are captured, which verifies the accuracy of the numerical results. [ABSTRACT FROM AUTHOR]

We develop a tri-state memristive system based on composable binarized memristors, from both a dynamical systems construction to the development of in-house fabricated devices. Firstly, based on the SPICE model of the binary memristor, the series and parallel circuits of binary memristors are designed, and the characteristics of each circuit are analyzed in detail. Secondly, through the analysis of the connection direction and parameters of the two binary memristors, an effective method to construct a tri-state memristor is proposed, and verified using SPICE simulations. Finally, the characteristics of the constructed equivalent tri-state memristor are analyzed, and it is concluded that the amplitude, frequency and type of the input signal can affect the characteristics of the equivalent tri-state memristor. Predictions from this modeling were validated experimentally using Au/ Nb 2 O 5 /Nb cross-point devices. [ABSTRACT FROM AUTHOR]

Reservoir computing (RC) has attracted much attention as a brain-like neuromorphic computing algorithm for time series processing. In addition, the hardware implementation of the RC system can significantly reduce the computing time and effectively apply it to edge computing, showing a wide range of applications. However, many hardware implementations of RC use different hardware to implement standard RC without further expanding the RC architecture, which makes it challenging to deal with relatively complex time series tasks. Therefore, we propose a bidirectional hierarchical light reservoir computing method using optoelectronic memristors as the basis for the hardware implementation. The approach improves the performance of hardware-implemented RC by allowing the memristor to capture multilevel temporal information and generate a variety of reservoir states. Ag | GQDs | TiOx | FTO memristors with negative photoconductivity effects can map temporal inputs nonlinearly to reservoir states and are used to build physical reservoirs to accomplish higher-speed operations. The method's effectiveness is demonstrated in multivariate time series classification tasks: a predicted accuracy of 98.44 % is achieved in voiceprint recognition and 99.70 % in the mobile state recognition task. Our study offers a strategy for dealing with multivariate time series classification issues and paves the way to developing efficient neuromorphic computing. [ABSTRACT FROM AUTHOR]

Locally-active memristors blessed with an edge-of-chaos domain, which can be destabilized for generating action potentials, are natural candidates for emulating biological neurons. Pinpointing the edge-of-chaos domain, where neuromorphic behaviors may occur, is important for studying neuromorphic dynamics of memristors. This paper proposes a short-cut method for locating the edge-of-chaos domains in two kinds of generic memristors, and in several typical memristive 1-port circuits using only the Jacobian matrix in terms of their equations. Taking the Chua Corsage Memristor (CCM) and several CCM-based memristive 1-port circuits as examples, we verify the proposed new methods, and calculates their edge-of-chaos domains. Also, we carry out a complete classification of all the parameter regions of the CCM and several CCM-based memristive 1-port circuits, namely the locally-passive, locally-active but unstable, and edge-of-chaos domains, under both voltage and frequency control. Near the calculated edge-of-chaos domain, we uncover some new neuromorphic behaviors. To confirm the physical interpretations and predictions of the edge-of-chaos theorem, this paper presents an inexpensive electronic circuit realization of the complete set of equations defining the CCM using only off-the-shelf circuit components. When this poor-man's memristor is connected to various linear passive R, L, C circuits, and a battery, the resulting circuit can be tuned to generate action potentials, and a garden variety of neuromorphic phenomena, including chaos. But the highlight of this paper is reserved for the CCM itself where the world's first oscilloscope picture of a contiguous self-intersecting triple-branch DC V–I curve of the CCM is displayed in real time. [ABSTRACT FROM AUTHOR]

Previous studies have shown that cyclic neural networks which have no autoexcitation and are unidirectional cannot generate chaos. Inspired by this finding, the present paper constructs a new memristive neural network composed of three nodes connected by the simplest circular loop, whose synaptic weights are replaced by hyperbolic memristors. The memristive neural network can generate chaos via period-doubling bifurcation, and generate different stable and periodic states with the variation of parameters. Another remarkable feature of the new memristive neural network is that it coexists with point and periodic attractors, periodic and chaotic attractors from different initial conditions. Detailed dynamic analysis and circuit implementation are given to illustrate the existence of chaos and coexisting attractors, which gives a positive answer to the interesting question whether chaos can occur in neural network with the simplest cyclic connections. [ABSTRACT FROM AUTHOR]

This paper presents a general modeling method for threshold-type multivalued memristors. Through this memristor modeling method, it is very simple to establish threshold-type memristor behavior models with different numbers of memristance elements, and these models are verified by numerical MATLAB simulations. A corresponding circuit-level SPICE model of the ternary memristor behavior model is developed and simulated in LTspice, shown to be consistent with the MATLAB results. Finally, the SPICE model is used to design the AND gate, OR gate, and three NOT gates of ternary state-based logic, and the effectiveness of the circuit is proved by LTSpice simulation. [ABSTRACT FROM AUTHOR]

This paper proposes a novel memristive chaotic circuit which originated from a Shinriki oscillator with two flux-controlled memristors of different polarities. This two-memristor-based Shinriki oscillator (TMSO) having a special plane equilibrium is prone to exhibiting the initial-dependent phenomenon of extreme multistability. To investigate its internal dynamics, a third-order dimensionality reduction model is established by utilizing the constitutive relationship of its memristor's flux and charge. The uncertain plane equilibrium is transferred into some deterministic model that can accurately predict the dynamical evolution of the system, where interesting phenomena of asymmetric bifurcations, extreme multistability and antimonotonicity are detected and analyzed by evaluating the position and stability of the equilibria in the flux–charge model. The simulation is carried out via Multisim to validate the analysis model, and the comparison of the phase trajectories, before and after dimensionality reduction, shows that this oscillator is good for research and practical use. [ABSTRACT FROM AUTHOR]

The nanoscale implementations of ternary logic circuits are particularly attractive because of high information density and operation speed that can be achieved by using emerging memristor technologies. Memristor is a nanoscale device with nonvolatility and adjustable multilevel states, which creates an intriguing opportunity for the implementation of ternary logic operations. This paper proposes a novel memristor-based design for stateful ternary logic, including AND, OR, NOT, NAND, NOR, and COPY operations. In the proposed memristor ternary logic (MTL) design, the resistance of memristor is the only logic state variable for representing the input and output. By sensing the value of the input memristors, the resistance of the output memristor changes accordingly. Furthermore, the MTL gates are not only capable of performing logic operations, but also storing logic values. To illustrate the potential of the methodology, a single-input-three-output ternary decoder is designed by using the proposed ternary logic circuits. Simulation results verify the effectiveness of the presented design. [ABSTRACT FROM AUTHOR]

Locally active memristors with multiple coexisting pinched hysteresis loops have attracted the attention of researchers. However, the currently reported multiple coexisting pinched hysteresis loops memristors are obtained by adding additional piecewise-linear terms into the original Chua corsage memristor. This paper proposes a novel locally active memristor by introducing a polynomial characteristic function into the state equation. The novel memristor has three coexisting pinched hysteresis loops, large relative range of active region and simple emulator circuit. The characteristics of the novel memristor such as power-off plot, coexisting pinched hysteresis loops and DC V – I plot are studied. The memristor is used in a Chua chaotic system to investigate the effects of locally active characteristic on the chaotic oscillation system. Furthermore, the memristor emulator and chaotic system are designed and implemented by commercial circuit elements. The hardware experiments are consistent with numerical simulations. [ABSTRACT FROM AUTHOR]

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 V – I plot and two asymptotically stable states (equilibrium points) on its power-off plot (POP) where voltage v = 0 , 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 V – I plot. Its dynamic characteristics are verified by theoretical analyses, simulations and DSP experiments. [ABSTRACT FROM AUTHOR]

Spontaneous electromagnetic induction originating from neuronal electrical activity is believed to reflect the memory ability in the neural system and significantly modulates neural information transmission, but its fundamental effect on the neuronal dynamic properties is still not well understood. In this paper, we use a memristor to couple neuronal electrical activity and magnetic fields and study how the spontaneous electromagnetic induction modulates the neuronal dynamical response to external stimulation. It is found that the negative feedback of electromagnetic induction on the neuron significantly reduces the dynamical response range, decreases the oscillation amplitude and induces a higher firing frequency. Meanwhile, the memory effect on electromagnetic induction can induce two kinds of bistability, including the coexistence of a stable limit cycle and a fixed point, and the coexistence of two stable limit cycles. Furthermore, high electric driving for electromagnetic induction produces complex firing patterns with single, double and multiple frequencies. Our results not only further confirm the efficacy of spontaneous electromagnetic induction in modulating the neuronal dynamical properties but also provide insights into the possibilities of choosing suitable parameter spaces in studying the effects of external magnetic induction on brain functions. [ABSTRACT FROM AUTHOR]

Memristor is a novel passive electronic element with resistance-switching dynamics. Due to the threshold property and the variable conductivity of the memristive element, its composite circuits are promising for the implementation of logic operations. In this paper, a flexible logic circuit based on the threshold-type memristor and the mature complementary metal-oxide-semiconductor (CMOS) technology is designed for the realization of Boolean logic operations. Specifically, the proposed method is able to perform the NAND, AND, OR, and NOR gate operations through two phases, i.e. the writing operation and the reading operation. In such implementation, the total delay is very small especially for time-sequence inputs. Furthermore, for existing memristor-based logic implementation, a contrastive analysis with relevant computer simulations is carried out. The experimental results indicate that the proposed method is capable of realizing all basic Boolean logic operations, and some more complicated cascaded logic operations with more compact circuit structures, higher efficiency, and lower operating cost. [ABSTRACT FROM AUTHOR]

Based on the definitions of fractional-order differential and Adomian decomposition algorithm, the numerical approximate solution of the incommensurate fractional-order memristor-based Chua's system is investigated. Dynamical characteristics of the proposed system are studied by using phase diagram, bifurcation analysis and power spectrum. Research results show that compared with the Adams–Bashforth–Moulton algorithm, the Adomian decomposition algorithm yields more accurate results and its solution generally converges more rapidly. Compared with 3.776 achieved by the Adams–Bashforth–Moulton algorithm, the minimum order of the incommensurate fractional-order memristor-based Chua's system solved by using Adomian decomposition algorithm is 1.76, which is much smaller. A reliable and efficient binary test for chaos, called "0–1 test", is utilized to detect the presence of chaotic attractors in the system dynamics. [ABSTRACT FROM AUTHOR]

Experimental study of a uni junction transistor (UJT) has enabled to show that this electronic component has the same features as the so-called "memristor". So, we have used the memristor's direct current (DC) v M – i M characteristic for modeling the UJT's DC current–voltage characteristic. This has led us to confirm on the one hand, that the UJT is a memristor and, on the other hand, to propose a new four-dimensional autonomous dynamical system allowing to describe experimentally observed phenomena such as the transition from a limit cycle to torus breakdown. [ABSTRACT FROM AUTHOR]

It is known that dynamical behaviors of memristive circuit are significantly affected by its initial states, which are difficult to be explicitly analyzed or controlled in voltage–current domain and have become great obstacles for its potential engineering applications. In this paper, the complex initial state-dependent dynamical behaviors of a physically realized memristive Chua's circuit are detailed and investigated using incremental flux-charge modeling method. This circuit is modeled in terms of incremental flux and charge, in which the original line equilibrium point is converted into some determined equilibrium points relying on the initial states of the dynamic elements. Moreover, the special initial state-dependent behaviors are transformed into system parameter-associated behaviors. Consequently, the detailed influences of each initial state, even the occurrence of hidden oscillations, can readily be theoretically interpreted. Finally, the initial state-dependent behaviors are physically captured and directed in the equivalent realization circuit of the incremental flux-charge model. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

In this paper, Chua’s circuit model with a fractional-order memristor is proposed and investigated from the viewpoint of nonlinear dynamics. Unlike the previous fractional-order models as generalizations of integer-order memristive Chua’s circuit in the literature, by replacing all the first-order derivatives in the system equation with fractional-order derivatives, the proposed model has only one fractional-order derivative in the system equation, introduced on the basis of a physical observation. Stability and bifurcation are analyzed for a sub-system, and numerical simulation is done for the whole circuit system. “Intermittent chaos” resulting from tangent bifurcation or grazing bifurcation is found numerically, for which limit cycle and chaotic attractor switch with very high frequency. This is a typical feature of nonsmooth dynamic systems, and the nonsmoothness is caused mainly by the fractional-order derivative. [ABSTRACT FROM AUTHOR]

In this paper, we designed a memristive spiking neural network (MSNN) to perform a fully functional Pavlov experiment. A memristor with forgetting effect is adopted to implement synapses while Izhikevich neurons are used for generating tonic spiking and tonic bursting signals. An asymmetric linear spiking time dependent plasticity (STDP) is naturally formed by taking into account the activation time difference between pre-synaptic neurons. Our design realizes associative, correcting, and forgetting processes without learning rule control modules. Moreover, an association will be enhanced if the activation time of two neurons is close enough, otherwise, all conditioned reflex associations will be weakened. [ABSTRACT FROM AUTHOR]

By replacing the resistor in a Twin-T network with a generalized flux-controlled memristor, this paper proposes a simple fourth-order memristive Twin-T oscillator. Rich dynamical behaviors can be observed in the dynamical system. The most striking feature is that this system has various periodic orbits and various chaotic attractors generated by adjusting parameter . At the same time, coexisting attractors and antimonotonicity are also detected (especially, two full Feigenbaum remerging trees in series are observed in such autonomous chaotic systems). Their dynamical features are analyzed by phase portraits, Lyapunov exponents, bifurcation diagrams and basin of attraction. Moreover, hardware experiments on a breadboard are carried out. Experimental measurements are in accordance with the simulation results. Finally, a multi-channel random bit generator is designed for encryption applications. Numerical results illustrate the usefulness of the random bit generator. [ABSTRACT FROM AUTHOR]

In this paper, the recent and emerging phenomenon of hidden oscillations is observed in a newly implemented memristor-based autonomous Duffing oscillator for the first time. The hidden oscillations are presented and quantified by various statistical measures. The system shows a large number of hidden attractors for a wide range of the system parameters. This study indicates that hidden oscillations can exist not only in piecewise-linear but also in smooth nonlinear circuits and systems. The distribution of Lyapunov exponents and the basin of attraction are explored to understand the nature of the hidden oscillations. We have also discussed the new phenomenon of periodic line invariant. An experimental demonstration is also presented using real time analog circuit. [ABSTRACT FROM AUTHOR]

Practical random number generation (RNG) circuits are typically achieved with analog devices or digital approaches. Digital-based techniques, which use field programmable gate array (FPGA) and graphics processing units (GPU) etc. usually have better performances than analog methods as they are programmable, efficient and robust. However, digital realizations suffer from the effect of finite precision. Accordingly, the generated random numbers (RNs) are actually periodic instead of being real random. To tackle this limitation, in this paper we propose a novel digital-analog hybrid scheme that employs the digital unit as the main body, and minimum analog devices to generate physical RNs. Moreover, the possibility of realizing the proposed scheme with only one memory element is discussed. Without loss of generality, we use the capacitor and the memristor along with FPGA to construct the proposed hybrid system, and a chaotic true random number generator (TRNG) circuit is realized, producing physical RNs at a throughput of Gbit/s scale. These RNs successfully pass all the tests in the NIST SP800-22 package, confirming the significance of the scheme in practical applications. In addition, the use of this new scheme is not restricted to RNGs, and it also provides a strategy to solve the effect of finite precision in other digital systems. [ABSTRACT FROM AUTHOR]

In this paper, a physical SBT memristor-based chaotic circuit is presented. The circuit dynamic behavior of dependence on the initial state of the SBT memristor and a key circuit parameter are investigated by theoretical analyses and numerical simulations. The results indicate that different initial states of the SBT memristor and the key circuit parameter can significantly impact the dynamic behavior of the chaotic circuit, such as stable sink, periodic cycle, chaos, and even some complex transient dynamics. It can guide future research on the realization of chaotic circuit based on physical SBT memristor. [ABSTRACT FROM AUTHOR]

Memristor is a nonlinear 'missing circuit element', that can easily achieve chaotic oscillation. Memristor-based chaotic systems have received more and more attention. Research shows that fractional-order systems are more close to real systems. As an important parameter, the order can increase the flexibility and degree of freedom of the system. In this paper, a fractional-order generalized memristor, which consists of a diode bridge and a parallel circuit with an equivalent unit circuit and a linear resistance, is proposed. Frequency and electrical characteristics of the fractional-order memristor are analyzed. A chain structure circuit is used to implement the fractional-order unit circuit. Then replacing the conventional Chua's diode by the fractional-order generalized memristor, a fractional-order memristor-based chaotic circuit is proposed. A large amount of research work has been done to investigate the influence of the order on the dynamical behaviors of the fractional-order memristor-based chaotic circuit. Varying with the order, the system enters the chaotic state from the periodic state through the Hopf bifurcation and period-doubling bifurcation. The chaotic state of the system has two types of attractors: single-scroll and double-scroll attractor. The stability theory of fractional-order systems is used to determine the minimum order occurring Hopf bifurcation. And the influence of the initial value on the system is analyzed. Circuit simulations are designed to verify the results of theoretical analysis and numerical simulation. [ABSTRACT FROM AUTHOR]

Dynamical phenomena in the parallel inductor-capacitor-memristor circuit are studied numerically. A systematic search for coexisting attractors is carried out. The existence of multiple attractors is observed and bifurcation diagrams are constructed. Basins of attraction are computed. The coexistence of attractors is proved using interval analysis tools. The existence of periodic attractors is confirmed by applying the interval Newton method to prove the existence of stable periodic orbits of an associated return map. For numerically observed chaotic attractors the existence of attractors is proved by constructing trapping regions enclosing chaotic trajectories of the return map. The existence of topological chaos is proved using the method of covering relations. [ABSTRACT FROM AUTHOR]

The SrBaTiO3 (SBT) memristor is prepared using the monolayer SrBaTiO3 nano-film structure. In order to apply it into the nonlinear circuit design, the SBT memristor is modeled in the paper. The voltage-controlled physical model of the SBT memristor is established based on its working mechanism. Due to the difficulty in determining the accurate parameters of the voltage-controlled physical model, a flux-controlled mathematical model of the SBT memristor is proposed, and its equivalence relation with the voltage-controlled physical model is proved. Moreover, the parameters of the flux-controlled mathematical model are determined by means of the quadratic polynomial interpolation method using the experimentally measured voltage and current data of the SBT memristor. The simulated - characteristic curve using the flux-controlled mathematical model coincides well with the measured - characteristic curves. The result indicates that the flux-controlled mathematical model with the definite parameters can be used to characterize the behaviors of the physical SBT memristor and guide its application to nonlinear circuit design. [ABSTRACT FROM AUTHOR]

We study a van der Pol-like memristor oscillator, obtained by substituting a Chua's diode with an active controlled memristor in a van der Pol oscillator with Chua's diode. The mathematical model for the studied circuit is given by a three-dimensional piecewise linear system of ordinary differential equations, depending on five parameters. We show that this system has a line of equilibria given by the -axis and the phase space is foliated by invariant planes transverse to this line, which implies that the dynamics is essentially two-dimensional. We also show that in each of these invariant planes may occur limit cycles and relaxation oscillations (that is, nonsinusoidal repetitive (periodic) solutions), depending on the parameter values. Hence, the oscillator studied here, constructed with a memristor, is also a relaxation oscillator, as the original van der Pol oscillator, although with a main difference: in the case of the memristor oscillator, an infinity of oscillations are produced, one in each invariant plane, depending on the initial condition considered. We also give conditions for the nonexistence of oscillations, depending on the position of the invariant planes in the phase space. [ABSTRACT FROM AUTHOR]

A memristor is the fourth circuit element, which has wide applications in chaos generation. In this paper, a four-dimensional hyperchaotic jerk system based on a memristor is proposed, where the scroll number of the memristive jerk system is controllable. The new system is constructed by introducing one extra flux-controlled memristor into three-dimensional multiscroll jerk system. We can get different scroll attractors by varying the strength of memristor in this system without changing the circuit structure. Such a method for controlling the scroll number without changing the circuit structure is very important in designing the modern circuits and systems. The new memristive jerk system can exhibit a hyperchaotic attractor, which has more complex dynamic behavior. Furthermore, coexisting attractors are observed in the system. Phase portraits, dissipativity, equilibria, Lyapunov exponents and bifurcation diagrams are analyzed. Finally, the circuit implementation is carried out to verify the new system. [ABSTRACT FROM AUTHOR]

In this paper, some complex nonlinear behaviors in a four-dimensional multiscroll autonomous memristor based chaotic system are investigated. This system is derived from the three-dimensional autonomous charge-controlled Muthuswamy-Chua simplest chaotic circuit. The system can generate four different coexisting attractors for a fixed set of parameters and different initial conditions. This phenomenon is relatively rare given that we have four different attractors namely: an equilibrium point, a stable limit cycle, a 16-peak limit cycle and a strange attractor that coexist in the system within a wide range of parameters. The nonlinear phenomenon of transient chaos is studied and revealed numerically in Matlab and Pspice environments. The complex transient dynamics of this memristive system under different initial states shows that the transient time depends strongly on the initial conditions. Moreover, this model displays spiking and bursting oscillations. The bursting behavior is classified according to the dynamics of separated slow and fast subsystems. It is shown to be of the fold-Hopf type. These complex dynamical behaviors of this system are investigated by means of numerical simulations and via Pspice circuit simulations. The use of bifurcation diagrams, Lyapunov exponents diagrams, power spectrums, phase portraits, time series, isospike diagram, basin of attraction, clearly shows these complex phenomena. [ABSTRACT FROM AUTHOR]

The Chua Corsage Memristor is the simplest example of a passive but locally active memristor endowed with two asymptotically stable equilibrium points and when powered by an E-volt battery, where . The basin of attraction is defined by , for , and , for . By adding an inductor of appropriate value in series with the battery, the resulting circuit undergoes a supercritical Hopf bifurcation and becomes an oscillator for . Applying a sinusoidal voltage source across the Chua corsage memristor, one finds two distinct coexisting stable periodic responses, depicted by their associated pinched hysteresis loops, of the same frequency whose basin of attraction is defined by , and , respectively, where depends on both amplitude A and frequency f. An in-depth and comprehensive analysis of the above global nonlinear phenomena is presented using tools from nonlinear circuit theory, such as Chua's dynamic route method, and from nonlinear dynamics, such as phase portrait analysis and bifurcation theory. [ABSTRACT FROM AUTHOR]

In this paper, an off-the-shelf memristor emulator of the quadratic memristor is developed and applied to a Lorenz circuit. The impulsive stabilization of the chaotic system by variable moments of impulses is investigated. By B-equivalence method, the considered variable-time impulsive system can be reduced to the fixed-time impulsive one. The simulations of the chaotic behavior verify the effectiveness of the emulator-based memristive system. The stability simulations support the validity of the method. [ABSTRACT FROM AUTHOR]

In this paper, we show that any -dimensional autonomous systems can be regarded as subsystems of -dimensional Hamiltonian systems. One of the two subsystems is identical to the -dimensional autonomous system, which is called the driving system. Another subsystem, called the response system, can exhibit interesting behaviors in the neighborhood of infinity. That is, the trajectories approach infinity with complicated nonperiodic (chaotic-like) behaviors, or periodic-like behavior. In order to show the above results, we project the trajectories of the Hamiltonian systems onto -dimensional spheres, or -dimensional balls by using the well-known central projection transformation. Another interesting behavior is that the transient regime of the subsystems can exhibit Chua corsage knots. We next show that generic memristors can be used to realize the above Hamiltonian systems. Finally, we show that the internal state of two-element memristor circuits can have the same dynamics as -dimensional autonomous systems. [ABSTRACT FROM AUTHOR]

Neurons can give appropriate response to external electrical stimuli and the modes in electrical activities can be carefully selected. Most of the neuron models mainly emphasize on the ion channel currents embedded into the membrane and the properties in electrical activities can be produced in the theoretical models. Indeed, some physical effect should be considered during the model setting for neuronal activities. In fact, induced current and the electrical field will cause the membrane potential to change and an exchange of charged ions during the fluctuation of ion concentration in cell. As a result, the effect of electromagnetic induction should be seriously considered. In this paper, magnetic flux is proposed to describe the effect of electromagnetic field, and the memristor is used to realize coupling on membrane by inputting induced current based on consensus of physical unit. Noise is also considered to detect the dynamical response in electrical activities and stochastic resonance, it is found that multiple modes can be selected in the electrical activities and it could be associated with memory effect and self-adaption in neurons. [ABSTRACT FROM AUTHOR]

In this paper, we consider a class of flux controlled memristive circuits with a piecewise linear memristor (i.e. the characteristic curve of the memristor is given by a piecewise linear function). The mathematical model is described by a discontinuous planar piecewise smooth differential system, which is defined on three zones separated by two parallel straight lines (called as discontinuity lines in discontinuous differential systems). We first investigate the stability of equilibrium points and the existence and uniqueness of a crossing limit cycle for the memristor-based circuit under self-excited oscillation. We then analyze the existence of periodic orbits of forced nonlinear oscillation for the memristive circuit with an external exciting source. Finally, we give numerical simulations to show good matches between our theoretical and simulation results. [ABSTRACT FROM AUTHOR]

In this paper, we investigate the global dynamics of a memristor oscillator which comes from [Corinto et al., 2011], where , and . Clearly, the case is trivial. So far, all results of this oscillator were given only for the case , where the set of equilibria may change among a singleton, three points and a singular continuum and at most one limit cycle can arise and no limit cycles arise from the continuum. Compared with the case , this oscillator displays more complicated dynamics for the case when . More clearly, one limit cycle may arise from the continuum and at most three limit cycles appear in the case of three equilibria, where generalized pitchfork bifurcation, saddle-node bifurcation, generalized Hopf bifurcation, double limit cycle bifurcation and homoclinic bifurcation may occur. Finally all global phase portraits are given for cases on the Poincaré disc, where a generalized normal sector method is applied. Moreover, our partial analytical results are demonstrated by numerical examples. [ABSTRACT FROM AUTHOR]

In recent years, memristor has become one of the research focuses. Considerable open literature has shown that many devices and systems possess memristive properties. Thus, research into supplying power source to these special devices and making them work steadily has been a meaningful study. This paper investigates the slow-scale instability whose oscillating frequency is between the line frequency and the switch frequency that occurs in a voltage controlled H-bridge inverter with memristive load. The mechanism of this medium-frequency oscillation is identified via harmonic balance method and Floquet theory. The results show that it is due to the occurrence of Hopf bifurcation. Finally, experimental results are presented to verify the theoretical analysis. [ABSTRACT FROM AUTHOR]

In this paper, a new memristor is proposed, and then an emulator built from off-the-shelf solid state components imitating the behavior of the proposed memristor is presented. Multisim simulation and breadboard experiment are done on the emulator, exhibiting a pinched hysteresis loop in the voltage-current plane when the emulator is driven by a periodic excitation voltage. In addition, a new simple chaotic circuit is designed by using the proposed memristor and other circuit elements. It is exciting that this circuit with only a linear negative resistor, a capacitor, an inductor and a memristor can generate a chaotic attractor. The dynamical behaviors of the proposed chaotic system are analyzed by Lyapunov exponents, phase portraits and bifurcation diagrams. Finally, an electronic circuit is designed to implement the chaotic system. For the sake of simple circuit topology, the proposed chaotic circuit can be easily manufactured at low cost. [ABSTRACT FROM AUTHOR]

This article introduces a novel four-dimensional autonomous multiscroll chaotic circuit which is derived from the actual simplest memristor-based chaotic circuit. A fourth circuit element - another inductor - is introduced to generate the complex behavior observed. A systematic study of the chaotic behavior is performed with the help of some nonlinear tools such as Lyapunov exponents, phase portraits, and bifurcation diagrams. Multiple scroll attractors are observed in Matlab, Pspice environments and also experimentally. We also observe the phenomenon of antimonotonicity, periodic and chaotic bubbles, multiple periodic-doubling bifurcations, Hopf bifurcations, crises and the phenomenon of intermittency. The chaotic dynamics of this circuit is realized by laboratory experiments, Pspice simulations, numerical and analytical investigations. It is observed that the results from the three environments agree to a great extent. This topology is likely convenient to be used to intentionally generate chaos in memristor-based chaotic circuit applications, given the fact that multiscroll chaotic systems have found important applications as broadband signal generators, pseudorandom number generators for communication engineering and also in biometric authentication. [ABSTRACT FROM AUTHOR]

The ion migration memristor is a nonlinear element with memory function and nanoscale size, it is considered as a potential candidate to reduce system power consumption and circuit size. When it works as the nonlinear part of the chaotic system, rich nonlinear curves will be produced, and at the same time, the complexity of chaotic systems and the randomness of signals will be enhanced. So in this paper, by Matlab numerical simulation, a new double-wing chaotic system based on an ion migration memristor is designed. In reality, there are many systems interfered inevitably by random noise, so in this paper the random bounded noises are also considered. The power spectrum, Lyapunov exponent spectrum, Poincaré map and bifurcation diagram are used to investigate its complex dynamic characteristics. Then, a SPICE-based analog circuit is presented to verify the feasibility of the system, for which the simulation results are consistent with the numerical simulation. Finally, the sliding mode variable structure control is applied to overcome the shortcomings of traditional control method, so that the chaotic orbits can be controlled to any fixed points or periodic orbits, and this provides an insight into chaos control in power electronics systems. [ABSTRACT FROM AUTHOR]

Memristive dynamics are generated utilizing active, weak-inversion, CMOS circuits. Class A and Class AB approaches to the generation of these dynamics are presented. The Class A circuit is composed of a grounded capacitor and two exponential transconductors (E-cells). It consumes a few nanowatts of power from a 1V power supply. The Class AB circuit also consists of a similar architecture with an added geometric mean splitter. Simulation results confirm the realization of pinched hysteresis loops exhibiting the zero crossing property of the memristor. The effects of varying input amplitude and frequency as well as the capacitor value are investigated. With the use of MOS capacitors in the place of monolithic capacitors, the area requirements of these emulators can be significantly diminished. Simulation results of circuits with both types of capacitors are presented. The simple emulators presented here offer the possibility of realizing nanoscale memristor dynamics when high yield memristor processes are not accessible. [ABSTRACT FROM AUTHOR]

An electronic oscillator circuit is designed by connecting an inductor in series with a locally-active PTC Memristor and a battery. The PTC Memristor is locally active on the negative resistance region of its DC - curve. A DC operating point is chosen on the locally-active region of the PTC Memristor and a small-signal equivalent circuit at is derived via Taylor series. The small-signal admittance of the composite one-port in Fig. 1 is derived using the small-signal equivalent circuit at , in series with an inductor whose value is chosen such that at some . The sinusoidal oscillation computed numerically from this circuit is shown to emerge from a supercritical Hopf bifurcation. [ABSTRACT FROM AUTHOR]

In this paper, we show that parasitic elements have a significant effect on the dynamics of memristor circuits. We first show that certain -terminal elements such as memristors, memcapacitors, and meminductors can be used as nonvolatile memories, if the principle of conservation of state variables hold by open-circuiting, or short-circuiting, their terminals. We also show that a passive memristor with a strictly-increasing constitutive relation will eventually lose its stored flux when we switch off the power if there is a parasitic capacitance across the memristor. Similarly, a memcapacitor (resp., meminductor) with a positive memcapacitance (resp., meminductance) will eventually lose their stored physical states when we switch off the power, if it is connected to a parasitic resistance. We then show that the discontinuous jump that circuit engineers assumed to occur at impasse points of memristor circuits contradicts the principles of conservation of charge and flux at the time of the discontinuous jump. A parasitic element can be used to break an impasse point, resulting in the emergence of a continuous oscillation in the circuit. We also define a distance, a diameter, and a dimension, for each circuit element in order to measure the complexity order of the parasitic elements. They can be used to find higher-order parasitic elements which can break impasse points. Furthermore, we derived a memristor-based Chua's circuit from a three-element circuit containing a memristor by connecting two parasitic memcapacitances to break the impasse points. We finally show that a higher-order parasitic element can be used for breaking the impasse points on two-dimensional and three-dimensional constrained spaces. [ABSTRACT FROM AUTHOR]

This paper deals with the problem of optimal synchronization of two identical memristive chaotic systems. We first study some basic dynamical properties and behaviors of a memristor oscillator with a simple topology. An electronic circuit (analog simulator) is proposed to investigate the dynamical behavior of the system. An optimal synchronization strategy based on the controllability functions method with a mixed cost functional is investigated. A finite horizon is explicitly computed such that the chaos synchronization is achieved at an established time. Numerical simulations are presented to verify the effectiveness of the proposed synchronization strategy. Pspice analog circuit implementation of the complete master-slave-controller systems is also presented to show the feasibility of the proposed scheme. [ABSTRACT FROM AUTHOR]

This paper addresses a systematic characterization of saddle-node bifurcations in nonlinear electrical and electronic circuits. Our approach is a circuit-theoretic one, meaning that the bifurcation is analyzed in terms of the devices' characteristics and the graph-theoretic properties of the digraph underlying the circuit. The analysis is based on a reformulation of independent interest of the saddle-node theorem of Sotomayor for semiexplicit index one differential-algebraic equations (DAEs), which define the natural context to set up nonlinear circuit models. The bifurcation is addressed not only for classical circuits, but also for circuits with memristors. The presence of this device systematically leads to nonisolated equilibria, and in this context the saddle-node bifurcation is shown to yield a bifurcation of manifolds of equilibria; in cases with a single memristor, this phenomenon describes the splitting of a line of equilibria into two, with different stability properties. [ABSTRACT FROM AUTHOR]

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 - curve. On the operating point, a small-signal equivalent circuit is derived via a Taylor series expansion. The small-signal admittance 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 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. [ABSTRACT FROM AUTHOR]

The generation of action potentials (oscillations) in biological systems is a complex, yet poorly understood nonlinear dynamical phenomenon involving ions. This paper reveals that the time-varying calcium ion and the time-varying potassium ion, which are essential for generating action potentials in Barnacle giant muscle fibers are in fact generic memristors in the perspective of electrical circuit theory. We will show that these two ions exhibit all the fingerprints of memristors from the equations of the Morris-Lecar model of the Barnacle giant muscle fibers. This paper also gives a textbook reference to understand the difference between memristor and nonlinear resistor via analysis of the potassium ion-channel memristor and calcium ion-channel nonlinear resistor. We will also present a comprehensive in-depth analysis of the generation of action potentials (oscillations) in memristive Morris-Lecar model using small-signal circuit model and the Hopf bifurcation theorem. [ABSTRACT FROM AUTHOR]

In this paper, a new fourth-order memristive chaotic system is constructed on the basis of Chua's circuit. Chaotic behaviors are verified through a series of dynamical analyses, including Lyapunov exponent analysis, bifurcation analysis, and phase diagram analysis. In addition, chaos attractors in the newly-proposed system are implemented by hardware circuits. [ABSTRACT FROM AUTHOR]