On the dynamics of chaotic circuits based on memristive diode-bridge with variable symmetry: A case study

In this paper, a practical equivalent circuit of an active flux-controlled memristor characterized by smooth piecewise-quadratic nonlinearity is designed and an experimental chaotic memristive circuit is implemented. The chaotic memristive circuit has an equilibrium set and its stability is dependent on the initial state of the memristor. The initial state-dependent and the circuit parameter-dependent dynamics of the chaotic memristive circuit are investigated via phase portraits, bifurcation diagrams and Lyapunov exponents. Both experimental and simulation results validate the proposed equivalent circuit realization of the active flux-controlled memristor.

This research explores the dynamics of an innovative three-degrees-of-freedom (3-DOF) spherical pendulum (SP) system integrated with a piezoelectric device to improve energy harvesting (EH) efficiency. The proposed model features a damped Duffing oscillator as the central component, coupled with a piezoelectric energy harvester and an attached SP. Lagrange’s equations are utilized to derive the system’s nonlinear differential governing equations. Analytical solutions (AS) are obtained using the multiple scales method (MSM) to achieve higher-order approximations. These solutions are then compared with numerical results to validate their accuracy and enhance the overall clarity of the analysis. Moreover, solvability criteria and characteristic exponents under resonant conditions are obtained. The stability of the steady-state solutions is analyzed using the Routh–Hurwitz criteria (RHC) and frequency response curves, providing deeper insights into the system’s behavior. Moreover, the basins of attraction have been simulated to analyze the behavior of the system’s nonlinear dynamics and its sensitivity to initial conditions. Additionally, the nonlinear stability analysis reveals both stable and unstable regimes, with resonance curves and time histories constructed for various parameter values. Furthermore, the phase portraits, graphs of bifurcation, and maps of Poincaré present a thorough view of the system’s dynamics that capture quasi-periodic and chaotic phenomena. This research has broad practical usages, evidenced by real-world applications of EH, including the power watch, power pucks, self-powered switches, Boeing wireless sensor nodes, and electrochemistry EH. The diversity and potential impact represented by these examples show the versatility of the proposed system in advancing EH technologies.

This paper focuses on the modeling and symmetry breaking analysis of the large class of chaotic electronic circuits utilizing an antiparallel diodes pair as nonlinear device necessary for chaotic oscillations. A new and relatively simple autonomous jerk circuit is used as a paradigm. Unlike current approaches assuming identical diodes (and thus a perfect symmetric circuit), we consider the more realistic situation where both antiparallel diodes present different electrical properties in spite of unavoidable scattering of parameters. Hence, the nonlinear component synthesized by the diodes pair exhibits an asymmetric current–voltage characteristic which engenders the explicit symmetry break of the whole electronic circuit. The mathematical model of the new circuit consists of a continuous time 3D autonomous system with exponential nonlinear terms. We investigate the chaos mechanism with respect to model parameters and initial conditions as well, both in the symmetric and asymmetric modes of operation by using bifurcation diagrams and phase space trajectories plots as main indicators. We report period doubling route to chaos, spontaneous symmetry breaking, merging crisis and the coexistence of two, four, or six mutually symmetric attractors in the symmetric regime of operation. More intriguing and complex nonlinear behaviors are revealed in the asymmetric system such as coexisting asymmetric bubbles of bifurcation (a new kind of phenomenon discovered in this work), hysteretic dynamics, critical phenomena, and coexisting multiple (i.e. two, three, four, or five) asymmetric attractors for some appropriately selected values of parameters. Laboratory experimental tests are conducted to support the theoretical analysis. The results obtained in this work clearly indicate that chaotic circuits with back to back diodes can demonstrate much more complex dynamics than what is reported in the relevant literature and thus should be reconsidered accordingly following the method described in this paper.

This paper proposes a multilevel inverter that produces many steps in output voltage using fewer power electronic switches. The configuration of the proposed inverter is modular and extendable. The suggested topology consists of a combination of series-connected switching units and a conventional H-bridge converter. The presented multilevel inverter is analyzed in both symmetric and asymmetric configurations. Two different methods to determine the size of DC voltage sources of the asymmetric configurations are presented to achieve the maximum steps in the output voltage. The characteristics of both symmetric and asymmetric configurations are given and compared together in detail. {#R1-2}The comparison results show that the asymmetric configuration with second design method uses less power switches and has less power losses than symmetric and first design method asymmetric configurations. However, it has more (Total Voltage Rating) TVR than two others. The comparison between symmetric configuration of the proposed multilevel inverter and four similar multilevel inverters shows that the proposed inverter uses fewer power switches and has less power losses. Finally, a laboratory prototype of the multilevel inverter is implemented and the experimental measurement results are given. The experimental measurement results validate proper operation of the proposed multilevel inverter.

Capturing and shunting energy in chaotic Chua circuit

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.

What is the simplest dissipative chaotic jerk equation which is parity invariant?

The classical attractors, defined as self-excited attractors, such as Lorenz attractor, Rssler attractor, Chua's attractor and many other well-known attractors, are all excited from unstable index-2 saddle-foci, namely, an attractor with an attraction basin corresponds to an unstable equilibrium. A new type of attractors, defined as hidden attractors, was first found and reported in 2011, whose attraction basin does not intersect with small neighborhoods of the equilibria of the system. Due to the existences of hidden attractors, some particular dynamical systems associated with line equilibrium, or no equilibrium, or stable equilibrium have attracted much attention recently. Additionally, by introducing memristors into existing oscillating circuits or substituting nonlinear resistors in classical chaotic circuits with memristors, a variety of memristor based chaotic and hyperchaotic circuits are simply established and has been broadly investigated in recent years. Motivated by these two considerations, in this paper, we present a novel memristive system with no equilibrium, from which an interesting and striking phenomenon of coexistence of the behaviors of hidden multiple attractors and the corresponding multistability is perfectly demonstrated by numerical simulations and experimental measurements. According to a newly proposed circuit realization scheme, a new type of four-dimensional memristive self-oscillated system is easily implemented by directly replacing a linear coupling resistor in an existing three-dimensional self-oscillated system circuit with a voltage-controlled memristor. The proposed system has no equilibrium, but can generate various hidden attractors including periodic limit cycle, quasi-periodic limit cycle, chaotic attractor, and coexisting attractors and so on. Based on bifurcation diagram, Lyapunov exponent spectra, and phase portraits, complex hidden dynamics with respect to a system parameter of the memristive self-oscillated system are studied. Specially, when different initial conditions are used, the system displays the coexistence phenomenon of chaotic attractors with different topological structures or quasi-periodic limit cycle and chaotic attractor, as well as the phenomenon of multiple attractors of quasi-periodic limit cycle and chaotic attractors with multiple topological structures. The results imply that some coexisting hidden multiple attractors reflecting the emergences of multistability can be observed in the proposed memristive self-oscillated system, which are well illustrated by several conventional dynamical analysis tools. Based on PSIM circuit simulation model, the memristive self-oscillated system is easily made in at a hardware level on a breadboard and two kinds of dynamical behaviors of coexisting hidden multiple attractors are captured in hardware experiments. Hardware experimental measurements are consistent with numerical simulations, which demonstrates that the proposed memristive self-oscillated system has very abundant and complex hidden dynamical characteristics.

A symmetric three-electrode configuration was applied to an anode-supported solid oxide fuel cell to study electrode polarization and the results were compared with those obtained via an asymmetric reference configuration. In this study, Ni/YSZ was used as the anode, LSM/YSZ as the cathode, Pt as the reference electrode, and thin YSZ film as the electrolyte. The cells were polarized potentiostatically at - 0.2 V, - 0.4 V, - 0.6 V and - 0.8 V with respect to open circuit voltage (OCV) and the potential changes of the anode and the cathode were measured via reference electrode simultaneously. The data from both symmetric and asymmetric configurations indicated cathode overpotentials was much larger than that observed on the anode. The cathode overpotentials decreased with increasing temperature. At low polarizations, cell overpotentials were disproportionately cathodic but the difference between anode and cathode polarization decreased with increasing polarization. The relative contribution of anodic overpotentials compared to cathodic was also observed to increase with increasing cell temperature.

Inverters have a wide range of applications in industries. Reduced switch topologies are current trend in multilevel inverters with reduced switching losses and improved total harmonic distortions. In this paper a new three phase multilevel inverter topology is proposed. The basic unit of proposed inverter in each phase generates a five level output under symmetric configuration and seven level output under asymmetrical configuration with 1:2 source ratio. The proposed inverter is modular in structure and a generalized circuit for n-levels is presented in this paper. The simulation of the proposed inverter is performed in MAT LAB/SI MULINK. The simulation results with symmetrical and asymmetrical configurations using single module and two modules is presented to validate the operation and modularity of the circuit.

In this paper, a novel approach of the KNOWM’s physical memristor behavior is introduced. It has been experimentally observed that this memristor, under certain conditions, can behave as a static nonlinear resistor. This inherent property of the KNOWM’s memristor prompts its use as a nonlinear reistor in chaotic circuits. Therefore, in this work, for the first time, the KNOWM memristor is used as a static nonlinear resistor in a well-known chaotic oscillator circuit. In order to examine circuit’s dynamical behavior a host of nonlinear simulation tools, such as phase portraits, bifurcation and continuation diagrams, as well as maximal Lyapunov exponent diagram, are used. Interesting phenomena related to chaos theory are observed. More specifically, period-doubling route to chaos, crisis phenomena, antimonotonicity, hysteresis and coexisting attractors, are investigated.

A novel chaotic system for generating multi-scroll attractors based on a Jerk circuit using a special form of a sine function (SFSF) is proposed in this paper, and the SFSF is the product of a sine function and a sign function. Although there are infinite equilibrium points in this system, the scroll number of the generated chaotic attractors is certain under appropriate system parameters. The dynamical properties of the proposed chaotic system are studied through Lyapunov exponents, phase portraits, and bifurcation diagrams. It is found that the scroll number of the chaotic system in the left and right part of the x-y plane can be determined arbitrarily by adjusting the values of the parameters in the SFSF, and the size of attractors is dominated by the frequency of the SFSF. Finally, an electronic circuit of the proposed chaotic system is implemented on Pspice, and the simulation results of electronic circuit are in agreement with the numerical ones.

A new multi-scroll Chua’s circuit with composite hyperbolic tangent-cubic nonlinearity: Complex dynamics, Hardware implementation and Image encryption application

This study investigates the problem of ecosystem dynamics in fragmented landscapes, specifically focusing on a two-patch environment with interacting prey and predators. The research examines the impact of cross-predation on these interactions. Using bifurcation analysis, we explored the structural arrangement of attractors and identified complex dynamics such as symmetric, asymmetric, and asynchronous attractors induced by varying cross-coupling levels. Notably, our study describes a novel mechanism for the formation of anti-phase synchrony in the patches. Unlike typical occurrences of a cycle following Hopf bifurcation, our model reveals that the anti-phase cycle stabilizes via Neimark-Sacker (NS) bifurcation of a two-period unstable cycle branch emanating from the synchronous cycle branch. Our findings also demonstrate that cross-feeding can lead to significant ecosystem asymmetry and branching, culminating in the dominance of a single cross-feeding chain. These results challenge traditional models and highlight the presence of multistability and the potential for ecosystem evolution towards distinct subsystem branches due to cross-predation. The study’s insights offer valuable contributions to population and evolutionary biology, enhancing our understanding of the intricate dynamics within fragmented ecosystems.

We evaluate the impact of temperature on the output behavior of a carbon nanotube field effect transistor (CNFET) based chaotic generator. The sources cause the variations in both current-voltage characteristics of the CNFET device and an overall chaotic circuit is pointed out. To verify the effect of temperature variation on the output dynamics of the chaotic circuit, a simulation is performed by employing the CNFET compact model of Wong et al. in HSPICE with a temperature range from −100°C to 100°C. The obtained results with time series, frequency spectra, and bifurcation diagram from the simulation demonstrate that temperature plays a significant role in the output dynamics of the CNFET-based chaotic circuit. Thus, temperature-related issues should be taken into account while designing a high-quality chaotic generator with high stability.