Explore the vast range of titles available.

When possessing a potential difference between two neurons, an electromagnetic induction current appears in the Hopfield neural network (HNN), which can be emulated by a flux-controlled memristor synapse. Thus, a three-order two-neuron-based autonomous memristive HNN is presented in this paper, which is the lowest order and has not been reported in the previous studies. With the mathematical model, the detailed stability analyses for the line equilibrium are executed, so that the fold and Hopf bifurcation sets and stability region distributions in the parameter plane are obtained. Furthermore, numerical results of coexisting bifurcation patterns are investigated, which are confirmed effectively by local basins of attraction and phase plane plots. The numerical results demonstrate coexisting multi-stable patterns of the spiral chaotic patterns with different dynamic amplitudes, periodic patterns with different periodicities, and stable resting patterns with different positions in the memristive HNN. Besides, the circuit synthesis and breadboard experiments are performed to well validate the numerical simulations.

Memristor, as a basic circuit component with strong nonlinearity, plays an important role in designing chaotic systems. In this study, three homogenous discrete memristors are coupled to establish a special triangular memristive network map (TMNM). The model has an infinite number of equilibrium points distributed in a three dimensional subspace, the generated attractors, thus, can be classified into hidden attractors. The dynamics related to coupling strength and initial condition of memristors are analyzed by dynamical maps, bifurcation diagrams, the Lyapunov exponents, and phase diagrams. As the coupling strength varies, the map exhibits two completely opposite bifurcation routes. The coexisting hyperchaotic, chaotic, quasi-periodic, and periodic attractors are observed under different initial conditions. In additional, partial and total amplitude control in this map can be respectively achieved by adjusting two independent system parameters. Without affecting the dynamic performance of the system, we introduce a constant controller in the original map to achieve signal polarity regulation. Finally, an image encryption scheme based on the TMNM is developed, and its security performance is verified by several evaluation criteria.

This paper investigates the dynamical responses and performances of mono-, bi-, and tri-stable nonlinear energy sinks in simultaneous vibration suppression and energy harvesting as well as solely vibration mitigation. To this end, a realizable multi-stable nonlinear energy sink composed of a bimorph cantilever beam and arrays of magnets is considered for vibration mitigation. The target vibrating structure is a simply-supported beam under a harmonic excitation. The proposed absorber can exhibit multi-stability based on the magnet gaps. First, using extended Hamilton’s principle, the coupled continuous magneto-electromechanical equations governing the system are obtained. Next, the bifurcations of the absorber fixed points that lead to different stability states are analyzed. Then, the time- and frequency-responses of the coupled system are studied using time integration. The results show that the bi- and tri-stable absorbers perform well in case of strongly modulated responses. Furthermore, the response of the coupled system is verified using the harmonic balance method and pseudo-arclength continuation. Next, the potential well escape method based on the harmonic balance solution is exploited to investigate the strongly modulated response emergence and disappearance as well as its variations with the system parameters. The coupling mechanism of the nonlinear absorber to the host beam is also studied using linearization and compared with the harmonic balance solution. In addition, in order to compare the performances of the bi-stable and tri-stable absorbers, energy-based analyses are performed. The results reveal the average harvested power per average kinetic energy of the main system for a bi-stable absorber is higher than a tri-stable absorber. Furthermore, the bi-stable absorber can mitigate the host structure vibration more than the tri-stable absorber. Finally, it is observed that the bi-stable absorber suppresses the vibration more than its corresponding mono-stable absorber and harvests more energy over a broader frequency region.

Freeplay is a common type of piecewise-smooth nonlinearity in dynamical systems, and it can cause discontinuity-induced bifurcations and other behaviors that may bring about undesirable and potentially damaging responses. Prior research has focused on piecewise-smooth systems with two or three distinct regions, but less attention is devoted to systems with more regions (i.e., multi-segmented systems). In this work, numerical analysis is performed on a dynamical system with multi-segmented freeplay, in which there are four stiffness transitions and five distinct regions in the phase space. The effects of the multi-segmented parameters are studied through bifurcation diagram evolution along with induced multi-stable behavior and different bifurcations. These phenomena are interrogated through various tools, such as harmonic balance, basins of attraction, phase planes, and Poincaré section analysis. Results show that among the three multi-segmented parameters, the asymmetry has the strongest effect on the response of the system.

It is sometimes difficult to model the stochastic differential equations for strongly nonlinear multi-stable vibration energy harvesters, especially for those under additive and multiplicative white noises, because of the existing challenges in quantifying noise intensities, nonlinear stiffness coefficients and damping coefficient. From the perspective of machine learning, a sparse identification method is devised to discover the general governing equation of energy harvester by using observed data on system state time series. With the observed data, the drift term and the diffusion term can be learned and then the stochastic differential equation can be identified. A penta-stable vibration energy harvester is taken as an example to verify the feasibility and effectiveness of the devised sparse identification method, which indicates that the method can be successfully applied to model the governing equation of a multi-stable vibration energy harvesting system under random excitation. Based on the learned data-driven stochastic differential equation for energy harvester, the stochastic dynamics can be further explored by appropriately adjusting the system parameters to improve energy harvesting performance and optimize the miniaturization design.

Soft robotics is an attractive and rapidly emerging field, in which actuation is coupled with the elastic response of the robot's structure to achieve complex deformation patterns. A crucial challenge is the need for multiple control inputs, which adds significant complication to the system. A novel concept of single‐input control of an actuator is proposed, which composes of interconnected bistable elements. Dynamic response of the actuator and predesigned differences between the elements are exploited to facilitate any desired multistate transition using a single dynamic input. Formulation and analysis of the control system's dynamics and pre‐design of its multiple equilibrium states, as well as their stability, are shown. Then, fabrication and demonstration are done experimentally on single‐input control of two‐ and four‐element actuators, where the latter can achieve transitions between up to 48 desired states. This work paves the way for next‐generation soft robotic actuators with minimal actuation and maximal dexterity. A concept for reducing the number of control inputs to one in a system with N degrees of freedom, is presented. Incorporating structural instabilities, cleverly, enables choosing any desired trajectory out of (N!)2 with only one input. The concept is demonstrated experimentally, along with analytical insights and numerical simulations. Such actuation ability will enable simpler, smaller, and cheaper robots.

The Kuroshio Current in the North Pacific displays path changes on an interannual‐to‐decadal time scale. In an idealized barotropic quasi‐geostrophic model of the double‐gyre wind‐driven circulation under stochastic wind‐stress forcing, such variability can occur due to transitions between different equilibrium states. The high‐dimensionality of the problem makes it challenging to determine the probability of these transitions under the influence of stochastic noise. Here we present a new method to estimate these transition probabilities, using a Dynamical Orthogonal (DO) field approach. In the DO approach, the solution of the stochastic partial differential equations system is decomposed using a Karhunen–Loève expansion and separate problems arise for the ensemble mean state and the so‐called time‐dependent DO modes. The original method is first reformulated in a matrix approach which has much broader application potential to various (geophysical) problems. Using this matrix‐DO approach, we are able to determine transition probabilities in the double‐gyre problem and to identify transition paths between the different states. This analysis also leads to the understanding which conditions are most favorable for transition. Plain Language Summary In an idealized wind‐driven double‐gyre circulation model of the midlatitude ocean circulation, a northward displaced jet (jet‐up state) and a southward displaced jet (jet‐down state) exist under the same forcing conditions. The existence of these states can help explain behavior of, for example, the Kuroshio Current in the North Pacific, which undergoes path variations on an interannual‐to‐decadal time scale. Under the influence of wind‐stress noise, the model circulation may undergo a transition between the jet‐up state to the jet‐down state and vice versa. Determining transition probabilities between the two states is challenging as the model has many degrees of freedom and transition probabilities are very small when the noise is low. In this paper, we use a new formulation of a model order reduction technique, the so‐called Dynamical Orthogonal (DO) field approach, to determine both transition probabilities and transition paths. Key Points A matrix version of the Dynamical Orthogonal (DO) field method is presented DO is used to determine transition probabilities in multi‐stable stochastic dynamical systems The method is applied to study transition behavior of ocean western boundary currents

Multi-stable systems, known for having complex nonlinear dynamics, have been shown in past studies to outperform their linear counterparts when designed for operation in vibration energy harvesters. This work investigates the dynamics and performance of a multi-stable electromagnetic energy harvesting device. The objectives are to enhance the levels of generated power and evaluate the useful bandwidths for the various modes of stability. Nonlinearity is introduced through a set of inclined springs and strongly influenced by the geometric parameters, as the shape of the potential energy curves can be adjusted by the selection of these properties. The effect of the geometric parameters’ uncertainties on the potential energy as a result of imperfections in manufacturing and installation, and the performance of the proposed harvester, is examined. A nominal tri-stable configuration is considered, and the sensitivity of the system to input design uncertainties is explored. The system’s response bifurcation diagrams and dynamical characteristics as well as the power output under up- and reverse-sweeping excitations are also reported. It is shown that the overall response and effectiveness of the nominal multi-stable harvester may drastically change in terms of resonance regions, periodicity of the motion, and levels of harvested power. A series of mono-stable and bi-stable harvesters arise due to the presence of geometrical uncertainties.

We consider one-dimensional reaction-diffusion equations for a large class of spatially periodic nonlinearities – including multi-stable ones – and study the asymptotic behavior of solutions with Heaviside type initial data. Our analysis reveals some new dynamics where the profile of the propagation is not characterized by a single front, but by a layer of several fronts which we call a terrace. Existence and convergence to such a terrace is proven by using an intersection number argument, without much relying on standard linear analysis. Hence, on top of the peculiar phenomenon of propagation that our work highlights, several corollaries will follow on the existence and convergence to pulsating traveling fronts even for highly degenerate nonlinearities that have not been treated before.

Electrically driven multi-stable cholesteric liquid crystals can be used to adjust the transmittance of incident light. Compared with the traditional liquid crystal optical devices, the multi-stable devices only apply an electric field during switching and do not require a continuous electric field to maintain the various optical states of the device. Therefore, the multi-stable devices have low energy consumption and have become a research focus for researchers. However, the multi-stable devices still have shortcomings before practical application, such as contrast, switching time, and mechanical strength. In this article, the latest research progress on electrically driven multi-stable cholesteric liquid crystals is reviewed, including electrically driven multi-stable modes, performance optimization, and applications. Finally, the challenges and opportunities of electrically driven multi-stable cholesteric liquid crystals are discussed in anticipation of contributing to the development of multi-stable liquid crystal devices.