Multistability Properties Research Articles

Aperture size control in kirigami metamaterials: Towards enhanced performance and applications

Kirigami metamaterials, inspired by the ancient art of kirigami, have recently emerged as an innovative approach for creating metamaterials with a diverse range of properties. While many studies on 2D kirigami have focused on stretchability and multi-stable properties, the variation in aperture size throughout the unfolding process of kirigami is another significant geometric feature. In this study, two novel kirigami materials are introduced, based on the topological construction of traditional triangular kirigami designs. These novel kirigami materials exhibit a wide range of aperture sizes, offering significant flexibility and tunability in stretch ratio. The diverse range of aperture sizes presents numerous potential applications at both micro and macro scales. Additionally, a hollow technique is proposed for designing kirigami cellular structures, which undergo distinct stages during the compression process characterized by low-reaction response and high-reaction response. This research expands the design possibilities of kirigami metamaterials by enabling precise adjustments in aperture sizes.

Chaos in chains: Exploring a novel supply chain model through bifurcation analysis, multi-stability and complete synchronization via backstepping control

Chaotic systems are highly sensitive to initial conditions, meaning small changes can lead to significant outcomes. This sensitivity can be leveraged to enhance the flexibility and adaptability of supply chains, allowing them to respond quickly to changing market demands and conditions. In this research work, we obtain a New Chaotic Supply Chain Model (NCSCM) by introducing a sinusoidal model uncertainty in the third differential equation of the Hamidzadeh chaotic supply chain model (2023). The sinusoidal uncertainty in the model accounts for the volatility and fluctuations of the supply chain model. We investigate the dynamic behaviors of NCSCM by performing a detailed Bifurcation Diagram (BD) analysis and Lyapunov Exponents (LEs). Next, we carry out a 0−1 test for the NCSCM to confirm the chaotic attractor of the system. We also study the multi-stability properties of the NCSCM. Finally, with the help of backstepping control, we derive new results for the complete synchronization of the novel chaotic supply chain models.

A review of curved crease origami: design, analysis, and applications

Origami structures with morphing behaviours and unique mechanical properties are useful in aerospace deployable structures, soft robots and mechanical metamaterials. Curved-crease origami, as one of the variants in the origami family, has a curve that connects two vertices as a crease compared to the straight crease counterpart. This feature couples the crease folding and facet bending during the folding process, providing versatile design space of mechanical metamaterials with tunable stiffness, multi-stability properties and morphing behaviours. However, current design techniques are mostly for simple geometries with intuitive construction, the modelling technique focuses on using the conventional finite element method, and the intrinsically complex geometries make specimens difficult to manufacture, which further hinders the development of curved-crease origami structures. Thus, it is valuable to review the state-of-the-art in curved-crease origami. This paper presents a review on the design methodology, analytical methods, and applications of curved-crease origami over the years, discusses their strengths, identifies future challenges and provides an outlook for the future development of the curved-crease origami concept.

A comprehensive study of the novel 4D hyperchaotic system with self-exited multistability and application in the voice encryption

This paper describes a novel 4-D hyperchaotic system with a high level of complexity. It can produce chaotic, hyperchaotic, periodic, and quasi-periodic behaviors by adjusting its parameters. The study showed that the new system experienced the famous dynamical property of multistability. It can exhibit different coexisting attractors for the same parameter values. Furthermore, by using Lyapunov exponents, bifurcation diagram, equilibrium points’ stability, dissipativity, and phase plots, the study was able to investigate the dynamical features of the proposed system. The mathematical model’s feasibility is proved by applying the corresponding electronic circuit using Multisim software. The study also reveals an interesting and special feature of the system’s offset boosting control. Therefore, the new 4D system is very desirable to use in Chaos-based applications due to its hyperchaotic behavior, multistability, offset boosting property, and easily implementable electronic circuit. Then, the study presents a voice encryption scheme that employs the characteristics of the proposed hyperchaotic system to encrypt a voice signal. The new encryption system is implemented on MATLAB (R2023) to simulate the research findings. Numerous tests are used to measure the efficiency of the developed encryption system against attacks, such as histogram analysis, percent residual deviation (PRD), signal-to-noise ratio (SNR), correlation coefficient (cc), key sensitivity, and NIST randomness test. The simulation findings show how effective our proposed encryption system is and how resilient it is to different cryptographic assaults.

Multi-dimensional phase portraits of stochastic fractional derivatives for nonlinear dynamical systems with solitary wave formation

This manuscript delves into the examination of the stochastic fractional derivative of Drinfel’d-Sokolov-Wilson equation, a mathematical model applicable in the fields of electromagnetism and fluid mechanics. In our study, the proposed equation is through examined through various viewpoints, encompassing soliton dynamics, bifurcation analysis, chaotic behaviors, and sensitivity analysis. A few dark and bright shaped soliton solutions, including the unperturbed term, are also examined, and the various 2D and 3D solitonic structures are computed using the Tanh-method. It is found that a saddle point bifurcation causes the transition from periodic behavior to quasi-periodic behavior in a sensitive area. Further analysis reveals favorable conditions for the multidimensional bifurcation of dynamic behavioral solutions. Different types of wave solutions are identified in certain solutions by entering numerous values for the parameters, demonstrating the effectiveness and precision of Tanh-methods. A planar dynamical system is then created using the Galilean transformation, with the actual model serving as a starting point. It is observed that a few physical criteria in the discussed equation exhibit more multi-stable properties, as many multi-stability structures are employed by some individuals. Moreover, sensitivity behavior is employed to examine perturbed dynamical systems across diverse initial conditions. The techniques and findings presented in this paper can be extended to investigate a broader spectrum of nonlinear wave phenomena.

Effects of Josephson junction synapse on coupled Morris-Lecar neurons

Recently, various artificial synapses have been examined in neural networks for obtaining different dynamical characteristics of neurons. The Josephson junction can be used for constructing an artificial synapse that incorporates the external magnetic field effects. Using the Josephson junction for coupling the neurons involves the phase error between the junctions. This paper uses the Josephson junction and a linear resistor to connect two Morris-Lecar neuron models. The effects of Josephson junction parameters are investigated on the dynamical properties of neurons. The obtained bifurcation and Lyapunov exponent diagrams represent that the Josephson junction synapse significantly affects the neurons’ dynamics. Rich dynamics are observed by varying the junction parameters. Moreover, the multistability properties are reported. Finally, the synchronization of coupled neurons is studied under different junction's parameters.

Research on Information Identification of Chaotic Map with Multi-Stability

Influenced by the rapid development of artificial intelligence, the identification of chaotic systems with intelligent optimization algorithms has received widespread attention in recent years. This paper focuses on the intelligent information identification of chaotic maps with multi-stability properties, and an improved sparrow search algorithm is proposed as the identification algorithm. Numerical simulations show that different initial values can lead to the same dynamic behavior, making it impossible to stably and accurately identify the initial values of multi-stability chaotic maps. An identification scheme without considering the initial values is proposed for solving this problem, and simulations demonstrate that the proposed method has the highest identification precision among seven existing intelligent algorithms and a certain degree of noise resistance. In addition, the above research reveals that chaotic systems with multi-stability may have more potential applications in fields such as secure communication.

A physical memristor-based chaotic system and its application in colour image encryption scheme

This work proposes a physical memristor (TaOx) based new 4D chaotic system with 3D multi-scroll, no equilibrium point, spiking behaviour, coexistence bursting oscillation and multistability. Using this physical memristor-based chaotic system, a novel and efficient colour image encryption algorithm has been developed using a unique box scrambling method and bit-wise XOR operations. Many interesting and new dynamics of a material-based memristive chaotic system are reported here, like 3D multi-scroll chaotic attractors, bursting characteristics, multistability, a neuronal system like spiking behaviours etc using Lyapunov spectrum and bifurcation plots. It is observed that the number of scrolls is changed with the total simulation time. This novel memristive chaotic system has limit cycles with controllable spikes and bursting oscillation. In addition, the system shows chaotic bursting oscillation under a different set of parameters and initial conditions. The coexistence of the bursting phenomena is studied here. The bursting and spiking characteristic is important for material-based memristors in neuromorphic applications. 3D Chaotic multi-scroll and multistability properties make the image encryption method more efficient and secure. Such characteristics are rare in physical memristor-based chaotic systems and using this, the image encryption algorithm is also rare in recent findings. Therefore, a new secure image encryption algorithm for colour images is proposed here, based on the unique box scrambling method, bitwise XOR operation and pseudo-random number generation using the proposed memristive chaotic system. Various tests like NPCR, UACI, histogram analysis, correlation study, information entropy analysis, robustness against external noise, etc have been performed to check the algorithm’s robustness and efficiency and test the capability to resist statistical and differential attacks.

Programmable Multi-stable Structure Based on Cosine Beam

Mechanical metamaterials with multi-stable properties are an emerging field of interest. In this paper, we present a novel 3D bi-stable cell element with negative stiffness characteristics designed based on a cosine-curved beam. Static compression simulations were performed for the single-cell model and the series model. Using “E” and “F” states as programming units, five array models were designed to analyze the stiffness variation rules. Dynamic simulations were conducted to compare the energy absorption rate and collision force of the model with variable stiffness. The conclusion shows that the structure has multi-stable and negative stiffness characteristics, and its stiffness can be adjusted in the range of 113.0 to 197.6 N/mm. Additionally, the energy absorption rate can be adjusted in the range of 8% to 65%. This study has made the structure configurable after manufacturing, breaking through the application limitations of predefined objects, and broadening its application prospects.

Reshape of the Bistable and Multistable Properties of Conical Structures Through Integrated Modification of Local Cross Section

Abstract Multistable structures can maintain multiple steady states without additional loads. However, the presence of geometric and material nonlinearities in multistable structures adds complexity and difficulty to their optimal design. In this paper, a novel method is proposed to achieve multistability in conical structures by local cross-section modification. A conical multistable structure with varying cross section is designed based on this method. The finite element model considering the nonlinear large deformation mechanics and rubber material’s hyperelasticity was established for analyzing the multistable properties and meanwhile verified by experiments. The influence of geometric parameters of the cross section (thickness, width, and position) on the multistabilities (number, distribution, and snapping threshold) was analyzed. The steady-state number can be effectively used to redesign the multistable properties by local reinforcement. It is also observed that the quasi-zero stiffness region of the force–displacement curve can be extended by 61.7% compared to the original conical structure. Moreover, the optimized QZS structure allows for an actively designable stepped dynamic response under forced vibration.

Design and Kinematics of Origami Inspired Non-Prismatic Foldable Truss Modules

Abstract Origami inspired deployable structures have received significant attention due to their exceptional kinematic and mechanical characteristics. Specifically, the cylindrical Kresling origami pattern has been extensively investigated for its multi-stable properties in past studies. This study presents the design and analysis of a novel non-prismatic foldable/deployable truss module inspired from the conical Kresling origami pattern. The intrinsic relationship between the kinematics and mechanics of non-prismatic foldable truss (NPFT) modules is investigated. First, the geometric design and the analytical modeling of the motion behavior of NPFT modules are presented, followed by the development of design maps considering a range of design parameters to demarcate the domains of qualitatively different deployment behavior. The numerical simulations were performed to validate the findings of analytical investigations. Later, the comparative analysis is presented to highlight the advancements of the proposed NPFT modules over conical Kresling truss structures. The programability of the deployment characteristics of NPFT modules is investigated considering different design parameters and the influence of scaling. The outcomes demonstrate that the proposed design of NPFT modules offers enhanced deployable and tunable properties along with ease of manufacturing for reconfigurable truss structures.

Five-state flexible dynamic windows

Flexible electrochromic (EC) devices are highly desirable in smart applications. Although flexible devices with up to three states have been demonstrated in previous work, the goal of EC device with characteristics of the multistate property, flexible compatibility, fast switching speed is still hard to achieve. In this work, we successfully developed a five-state flexible dynamic window (FFDW) based on Bi and Cu bimetal reversibly deposited system. This device possesses transparent state, gray state, black state, cupreous mirror state and silvery mirror state via a precise voltage control strategy. More excitingly, the phenomenon of two mirror states obtained in one device is firstly reported. This FFDW, which can be bended for more than 50 times, exhibits fast switching speed of 2.34 s for complete stripping and 11.12 s for tinting, with a more than 63% transmittance modulation range at black state and an over 60% reflectance modulation range at mirror state. Finally, we unveiled the mechanism accounting for the voltage-dependent rich optical states in details. Our findings are helpful for developing high-performance dynamic windows for application in smart homes, vehicles and wearable devices.

A negative stiffness structure with multi-stable characteristic

This work proposes a straw-shaped structure (SS) inspired by the folds of straw. Two samples named SSⅠ and SSⅡ with 5 and 5.5 layers of conical structures, respectively, are prepared using selective laser sintering (SLS) technology. SSⅠ and SSⅡ can spontaneously recover to their original shapes after compression experiments. With the thickness of 0.6 and 3.0 mm for the upper and lower parts of cells, the peak and valley forces of SSII (SS-3.0-0.6) during compression and tension alternate periodically. The first and second valley forces of SS-3.0-0.6 are −16.1 and −20.2 N during compression, and its second, fifth and fourth peak forces are 30.2, 4.3 and 0.8 N during tension. SS-3.0-0.6 exhibits significant NS and multi-stable properties in both compression and tension, and it is easier to be stretched than compressed. The deformation mode of the folded structure is similar to stacked porcelain bowls. Through a reasonable design of geometric parameters, the folding order and deformation mode as well as the number of stable state of the SSII models can be customized. In addition, the potential applications of SSs are also discussed, and this work provides a valuable reference for the study of NS structures.

TWO DISCRETE MEMRISTIVE CHAOTIC MAPS AND ITS DSP IMPLEMENTATION

In this paper, a discrete model of memristor is adopted and analyzed. The new discrete maps are built by introducing this discrete memristor model into a two-dimensional discrete map. Interestingly, introducing this discrete memristor model from different locations can lead to two new chaotic map models. The dynamical behaviors of the two maps are studied by means of bifurcation diagrams, phase diagrams and Lyapunov exponential spectra (LEs). The simulation results show that both chaotic systems have rich dynamical behaviors. In addition, they are experimentally found to have multi-stable properties, where the M-XM map has infinite attractors coexistence. Finally, we complete the hardware implementation of the two maps based on Digital Signal Processing (DSP) platform for the application of discrete chaotic systems.

Embedding the Dynamics of Forced Nonlinear Systems in Multistable Memristor Circuits

A well-known feature of memristors is that they makes the circuit dynamics much richer than that generated by classical <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$RLC$ </tex-math></inline-formula> circuits containing nonlinear resistors. In the case of circuits with ideal memristors, such a multistability property, i.e., the coexistence of many different attractors for a fixed set of parameters, is connected to the fact that the state space is composed of a continuum of invariant manifolds where either convergent or oscillatory and more complex behaviors can be displayed. In this paper we investigate the possibility of designing memristor circuits where known attractors are embedded into the invariant manifolds. We consider a class of forced nonlinear systems containing several systems which are known to display complex dynamics, and we investigate under which conditions the dynamics of any given system of the class can be reproduced by a circuit composed of a two-terminal (one port) element connected to a flux-controlled memristor. It is shown that an input-less circuit is capable to replicate the system attractors generated by varying the constant forcing input, once the parameters of the two-terminal element and the memristor nonlinear characteristic are suitably selected. Indeed, there is a one-one correspondence between the dynamics generated by the nonlinear system for a constant value of the input and that displayed on one of the invariant manifolds of the input-less memristor circuit. Some extensions concerning the case of non-constant forcing terms and the use of charge-controlled memristors are also provided. The results are illustrated via FitzHugh-Nagumo model and Duffing oscillator.

Multistability, symmetry and geometric conservation in eightfold waterbomb origami

The nonlinearities inherent in the mechanics of origami make it a rich design space for multistable structures and mechanical metamaterials. Here, we investigate the multistability of a classic origami base: the symmetric eightfold waterbomb. We prove that the waterbomb is bistable for certain crease properties, and derive bounds on, and closed-form approximations of, its stable states. We introduce a simplified form of the waterbomb kinematics and present a design procedure for tuning the depth and the symmetry/asymmetry of its energy wells. By incorporating the concept of pretensioned torsional springs, we also demonstrate the existence of tristable cases for the waterbomb fold pattern. We then apply the analysis of a single waterbomb to study quasi-one-dimensional arrays of waterbombs, where we discover a conserved geometric-kinematic quantity in which the number of popped-up and popped-down vertices is determined uniquely through analysis of the origami structure’s boundaries. This culminates with a discussion of how the quasi-one-dimensional array may be designed to achieve stable states with various degeneracies, kinematics and gaps between energy levels. Collectively, this work presents an alternative approach for characterizing origami multistability properties and reveals an origami design motif that has potential applications in physically reconfigurable structures, mechanical energy absorption and metamaterials.

Design of heterogeneous time-lags system with multi-stability and its analog circuit

A novel heterogeneous time-lags chaotic system is constructed and explored in this work. By choosing appropriate control parameters, the state of this system can be switched between conservative and dissipative. When different initial conditions are selected, this system can produce multiple coexisting attractors or flows, that is, the system has the property of multi-stability. More interestingly, the attractors generated by this system can be distributed in 1-D lines, 2-D lattices and 3-D grids which means the circumstance of multi-directional attractors occurs. And the rare phenomenon of transient chaos is analyzed in this system as well. It is worth noting that the implementation of hardware circuits for time-lags chaotic systems has been a major obstacle in engineering applications. To remove this bottleneck and further explore the physical presence of this proposed system, the hardware analog circuit of the proposed system is achieved. The experimental observations further verify the feasibility of this system. Additionally, the experiments of spectral entropy complexity and image encryption performance verify the good performance of the proposed system.

Coexistence of ferroelectric phases in barium titanate single-domain thin films

In about twenty years, the temperature-misfit strain phase diagrams have become valuable tools to describe ferroelectric thin film properties. The background theoretical approach consists in searching for the position of the global minimum of the potential landscape and deducing the thermodynamically stable phase. In temperature-misfit strain phase diagrams, lines separate the stable phase regions, and the analysis of the polarization continuity properties across these lines allows us to determine the order of phase transition. This work revealed additional important information relative to the properties of first order phase transitions; we determined the limit of stability of the metastable phases and plotted the corresponding lines in the traditional temperature-misfit strain diagrams. These one dimensional boundaries are the analog to the superheating and supercooling temperature points in the context of bulk ferroelectric crystal. We highlight two dimensional coexistence regions adjacent to first order thermodynamic transition lines. The location and the shape of these regions are strongly dependent on the set of parameters used to describe the bulk crystal. We illustrate the interest in the revelation of coexistence regions, showing that the corresponding multi-stability properties could be used to design non-binary memory cells by using barium titanate thin films.

A metafluid with multistable density and internal energy states

Investigating and tailoring the thermodynamic properties of different fluids is crucial to many fields. For example, the efficiency, operation range, and environmental safety of applications in energy and refrigeration cycles are highly affected by the properties of the respective available fluids. Here, we suggest combining gas, liquid and multistable elastic capsules to create an artificial fluid with a multitude of stable states. We study, theoretically and experimentally, the suspension’s internal energy, equilibrium pressure-density relations, and their stability for both adiabatic and isothermal processes. We show that the elastic multistability of the capsules endows the fluid with multistable thermodynamic properties, including the ability of capturing and storing energy at standard atmospheric conditions, not found in naturally available fluids.

A memristive conservative chaotic circuit with two different offset boosting behaviors

Recent studies have shown that more complex dynamics could be observed if memristors are coupled into nonlinear circuits. To date, however, far too little attention has been paid to memristor-based high-dimensional conservative systems. Previous research on the low-dimensional mem-element system has suffered from a paucity of rich dynamical characteristics. In addition, the physical implementation of conservative systems requires higher accuracy than dissipative ones, and no DSP implementation of a memristor-based conservative system is available. In this paper, a high-dimensional memristive conservative system is built by coupling the linear resistance of a conservative chaotic circuit with a flux-controlled memristor. Compared to the existing conservative systems, the proposed system exhibits a variety of quasi-periodic topologies and has two offset boosting behaviors. One of the constant variable offset boosting also presents meaningful parameter space expansion characteristics. And the other initial offset boosting exhibits homomorphic and heteromorphic multistability properties. Moreover, our work also reveals that transient chaos is the route to chaos in conservative systems. Finally, analog circuit simulation and DSP-based digital circuits verify the correctness of the numerical calculation and the physical implementations of the system.