Reprogramming multi-stable snapping and energy dissipation in origami metamaterials through panel confinement.

With a focus on a class of origami-inspired metamaterials, this work explores the role of panel confinement in their mechanical response under cyclic loading. The goal is twofold: (i) quantify the magnitude change in snapping force and energy dissipation attained by varying the severity of confinement of selected panels; and (ii) leverage insights to modulate in situ their mechanical response as dictated by a given application, hence propose panel confinement modulation as a practical design route for response reprogrammability. Through computational modelling, proof-of-concept fabrication and cyclic testing, we first identify and characterize the governing factors enabling either the alteration or the preservation of the snapping force magnitude during repeated cycles of forward and backward loading. Then, we demonstrate how the in situ modulation of the constrained distance between selected panels enables reprogramming their snapping sequence and energy dissipation. The results contribute to expanding the versatility and application of this class of origami metamaterial across sectors, from aerospace to protective equipment, requiring precise control of mechanical damping and energy dissipation.This article is part of the theme issue 'Origami/Kirigami-inspired structures: from fundamentals to applications'.

Intrinsically Multi-Stable Spatial Linkages.

Multi-stable structures can be reconfigured with fewer, lightweight, and less accurate actuators. This is because the attraction domain in the multi-stable energy landscape provides both reconfiguration guidance and shape accuracy. Additionally, such structures can generate impulsive motion due to structural instability. Most multi-stable units are planar structures, while spatial linkages can generate complex 3D motion and hold a more promising potential for applications. This study proposes a generalized approach to design a type of intrinsically multi-stable spatial (IMSS) linkages with multiple prescriptible configurations, which are structurally compatible, and naturally stable at these states. It reveals that all over-constrained mechanisms can be transformed into multi-stable structures with the same design method. Single-loop bi-stable 4R and quadra-stable 6R spatial linkages modules with intrinsic non-symmetric stable states, which are transformed from fundamental kinematic linkage mechanisms unit such as Bennett and Bricard linkages, are designed to illustrate the basic idea and the superiority over the ordinary methods. Multi-loop assembly by these IMSS linkage modules shows potential for practical applications that are required for the deployability and impulsivity of reconfiguration. Two preliminary design cases of a deployable tube and an impulsive gripper are experimentally presented to validate this applicability. Further promisingly, this design method of IMSS linkages paves the way for morphing platforms with lightweight actuation, high shape accuracy, high stiffness, and prescribed impulsive 3D motion.

Multistability and fixed-time multisynchronization of switched neural networks with state-dependent switching rules.

This paper presents theoretical results on the multistability and fixed-time synchronization of switched neural networks with multiple almost-periodic solutions and state-dependent switching rules. It is shown herein that the number, location, and stability of the almost-periodic solutions of the switched neural networks can be characterized by making use of the state-space partition. Two sets of sufficient conditions are derived to ascertain the existence of 3n exponentially stable almost-periodic solutions. Subsequently, this paper introduces the novel concept of fixed-time multisynchronization in switched neural networks associated with a range of almost-periodic parameters within multiple stable equilibrium states for the first time. Based on the multistability results, it is demonstrated that there are 3n synchronization manifolds, wherein n is the number of neurons. Additionally, an estimation for the settling time required for drive-response switched neural networks to achieve synchronization is provided. It should be noted that this paper considers stable equilibrium points (static multisynchronization), stable almost-periodic orbits (dynamical multisynchronization), and hybrid stable equilibrium states (hybrid multisynchronization) as special cases of multistability (multisynchronization). Two numerical examples are elaborated to substantiate the theoretical results.

Dynamics of pH Oscillators in Continuous Stirred Tanks in Series.

Complex reaction networks with positive and negative feedback can produce diverse nonlinear phenomena in open reactors, such as multistability and oscillations. pH oscillators driven by hydrogen or hydroxide autocatalytic processes show sustained oscillations in continuously stirred tank reactors (CSTR) but only a sharp pH switch in batch. Here, we present a numerical study on the dynamics of pH oscillators in a series of CSTRs. We show a critical residence time under which bistability and above which oscillations develop. The dynamics of the CSTR cascade show the cross-shaped phase diagram of nonlinear activatory inhibitory systems. In the domain of oscillations, one reactor starts to oscillate autonomously and induces forced complex oscillations in the following tanks with damped amplitudes. These results, with their practical implications, may contribute to understanding the recent experimental observations of nonlinear phenomena in the presence of a residence time ramp and inspire further research in this area.

The interplay of facilitation and competition drives the emergence of multistability in dryland plant communities.

Within communities, species are wrapped in a set of feedbacks with each other and with their environment. When such feedbacks are strong enough they can generate alternative stable states. So far, research on alternative stable states has mostly focused on systems with a small number of species and a limited diversity of interaction types. Here, we analyze a spatial model of plant community dynamics in stressed ecosystems such as drylands, where each species is characterized by a strategy, and the different species interact through facilitation and competition for space and resources, such as water. We identify three different types of multistability emerging from the interplay of competition and facilitation. Under low-stress levels, plant communities organize in small groups of coexisting species, maintained by space, competition and facilitation ("cliques"). Under higher stress levels, positive feedback from facilitation lead to the dominance of a single facilitating species ("mutual exclusion states"). At the highest stress levels, the single facilitating species left in the system coexists with the desert state. By linking community ecology and alternative stable states theory using a spatial plant community model for stressed ecosystems, our study contributes to highlight the importance of positive feedback loops for the stability of ecological communities.

Unified analysis on multistablity of fraction-order multidimensional-valued memristive neural networks.

This article provides a unified analysis of the multistability of fraction-order multidimensional-valued memristive neural networks (FOMVMNNs) with unbounded time-varying delays. Firstly, based on the knowledge of fractional differentiation and memristors, a unified model is established. This model is a unified form of real-valued, complex-valued, and quaternion-valued systems. Then, based on a unified method, the number of equilibrium points for FOMVMNNs is discussed. The sufficient conditions for determining the number of equilibrium points have been obtained. By using 1-norm to construct Lyapunov functions, the unified criteria for multistability of FOMVMNNs are obtained, these criteria are less conservative and easier to verify. Moreover, the attraction basins of the stable equilibrium points are estimated. Finally, two numerical simulation examples are provided to verify the correctness of the results.

Multistability of segmented rings by programming natural curvature.

Multistable structures have widespread applications in the design of deployable aerospace systems, mechanical metamaterials, flexible electronics, and multimodal soft robotics due to their capability of shape reconfiguration between multiple stable states. Recently, the snap-folding of rings, often in the form of circles or polygons, has shown the capability of inducing diverse stable configurations. The natural curvature of the rod segment (curvature in its stress-free state) plays an important role in the elastic stability of these rings, determining the number and form of their stable configurations during folding. Here, we develop a general theoretical framework for the elastic stability analysis of segmented rings (e.g., polygons) based on an energy variational approach. Combining this framework with finite element simulations, we map out all planar stable configurations of various segmented rings and determine the natural curvature ranges of their multistable states. The theoretical and numerical results are validated through experiments, which demonstrate that a segmented ring with a rectangular cross-section can show up to six distinct planar stable states. The results also reveal that, by rationally designing the segment number and natural curvature of the segmented ring, its one- or multiloop configuration can store more strain energy than a circular ring of the same total length. We envision that the proposed strategy for achieving multistability in the current work will aid in the design of multifunctional, reconfigurable, and deployable structures.

Unveiling serotonergic dysfunction of obsessive-compulsive disorder on prefrontal network dynamics: a computational perspective.

Serotonin (5-HT) regulates working memory within the prefrontal cortex network, which is crucial for understanding obsessive-compulsive disorder. However, the mechanisms how network dynamics and serotonin interact in obsessive-compulsive disorder remain elusive. Here, we incorporate 5-HT receptors (5-HT1A, 5-HT2A) and dopamine receptors into a multistable prefrontal cortex network model, replicating the experimentally observed inverted U-curve phenomenon. We show how the two 5-HT receptors antagonize neuronal activity and modulate network multistability. Reduced binding of 5-HT1A receptors increases global firing, while reduced binding of 5-HT2A receptors deepens attractors. The obtained results suggest reward-dependent synaptic plasticity mechanisms may attenuate 5-HT related network impairments. Integrating serotonin-mediated dopamine release into circuit, we observe that decreased serotonin concentration triggers the network into a deep attractor state, expanding the domain of attraction of stable nodes with high firing rate, potentially causing aberrant reverse learning. This suggests a hypothesis wherein elevated dopamine concentrations in obsessive-compulsive disorder might result from primary deficits in serotonin levels. Findings of this work underscore the pivotal role of serotonergic dysregulation in modulating synaptic plasticity through dopamine pathways, potentially contributing to learned obsessions. Interestingly, serotonin reuptake inhibitors and antidopaminergic potentiators can counteract the over-stable state of high-firing stable points, providing new insights into obsessive-compulsive disorder treatment.

An analytical approach to engineer multistability in the oscillatory response of a pulse-driven ReRAM.

A nonlinear system, exhibiting a unique asymptotic behaviour, while being continuously subject to a stimulus from a certain class, is said to suffer from fading memory. This interesting phenomenon was first uncovered in a non-volatile tantalum oxide-based memristor from Hewlett Packard Labs back in 2016 out of a deep numerical investigation of a predictive mathematical description, known as the Strachan model, later corroborated by experimental validation. It was then found out that fading memory is ubiquitous in non-volatile resistance switching memories. A nonlinear system may however also exhibit a local form of fading memory, in case, under an excitation from a given family, it may approach one of a number of distinct attractors, depending upon the initial condition. A recent bifurcation study of the Strachan model revealed how, under specific train stimuli, composed of two square pulses of opposite polarity per cycle, the simplest form of local fading memory affects the transient dynamics of the aforementioned Resistive Random Access Memory cell, which, would asymptotically act as a bistable oscillator. In this manuscript we propose an analytical methodology, based on the application of analysis tools from Nonlinear System Theory to the Strachan model, to craft the properties of a generalised pulse train stimulus in such a way to induce the emergence of complex local fading memory effects in the nano-device, which would consequently display an interesting tuneable multistable oscillatory response, around desired resistance states. The last part of the manuscript discusses a case study, shedding light on a potential application of the local history erase effects, induced in the device via pulse train stimulation, for compensating the unwanted yet unavoidable drifts in its resistance state under power off conditions.

Tuning the Properties of Multi-Stable Structures Post-Fabrication Via the Two-Way Shape Memory Polymer Effect.

Multi-stable elements are commonly employed to design reconfigurable and adaptive structures, because they enable large and reversible shape changes in response to changing loads, while simultaneously allowing self-locking capabilities. However, existing multi-stable structures have properties that depend on their initial design and cannot be tailored post-fabrication. Here, a novel design approach is presented that combines multi-stable structures with two-way shape memory polymers. By leveraging both the one-way and two-way shape memory effect under bi-axial strain conditions, the structures can re-program their 3D shape, bear loads, and self-actuate. Results demonstrate that the structures' shape and stiffness can be tuned post-fabrication at the user's need and the multi-stability can be suppressed or activated on command. The control of multi-stability prevents undesired snapping of the structures and enables higher load-bearing capability, compared to conventional multi-stable systems. The proposed approach offers the possibility to augment the functionality of existing multi-stable concepts, showing potential for the realization of highly adaptable mechanical structures that can reversibly switch between being mono and multi-stable and that can undergo shape changes in response to a change in temperature.

Parietal theta burst TMS does not modulate bistable perception.

The role of the parietal cortex in perceptual awareness and in resolving perceptual ambiguity is unsettled. Early influential transcranial magnetic stimulation studies have revealed differences in conscious perception following parietal stimulation, fuelling the notion that parietal cortex causally contributes to resolving perceptual ambiguity. However, central to this conclusion is the reliability of the method employed. Several prior studies have revealed opposing effects, such as shortening, lengthening, or no effect on multistable perceptual transitions following parietal stimulation. Here we addressed the reliability of continuous theta-burst stimulation (cTBS) on parietal cortex on the perception of bistable stimuli. We conducted three cTBS experiments that were matched to prior experiments in terms of stimuli, stimulation protocol, and target site, and used a higher number of participants. None of our cTBS experiments replicated prior cTBS results. The only experiment using individual functional localizers led to weak effects, while the two others led to null results. Individual variability of motor cortex cTBS did not predict parietal cTBS effects. In view of recent reports of highly variable cTBS effects over motor cortex, our results suggest that cTBS is particularly unreliable in modulating bistable perception when applied over parietal cortex.

Intrinsically Multistable Soft Actuator Driven by Mixed-Mode Snap-Through Instabilities.

Actuators utilizing snap-through instabilities are widely investigated for high-performance fast actuators and shape reconfigurable structures owing to their rapid response and limited reliance on continuous energy input. However, prevailing approaches typically involve a combination of multiple bistable actuator units and achieving multistability within a single actuator unit still remains an open challenge. Here, a soft actuator is presented that uses shape memory alloy (SMA) and mixed-mode elastic instabilities to achieve intrinsically multistable shape reconfiguration. The multistable actuator unit consists of six stable states, including two pure bending states and four bend-twist states. The actuator is composed of a pre-stretched elastic membrane placed between two elastomeric frames embedded with SMA coils. By controlling the sequence and duration of SMA activation, the actuator is capable of rapid transition between all six stable states within hundreds of milliseconds. Principles of energy minimization are used to identify actuation sequences for various types of stable state transitions. Bending and twisting angles corresponding to various prestretch ratios are recorded based on parameterizations of the actuator's geometry. To demonstrate its application in practical conditions, the multistable actuator is used to perform visual inspection in a confined space, light source tracking during photovoltaic energy harvesting, and agile crawling.

Turing Instabilities are Not Enough to Ensure Pattern Formation.

Symmetry-breaking instabilities play an important role in understanding the mechanisms underlying the diversity of patterns observed in nature, such as in Turing's reaction-diffusion theory, which connects cellular signalling and transport with the development of growth and form. Extensive literature focuses on the linear stability analysis of homogeneous equilibria in these systems, culminating in a set of conditions for transport-driven instabilities that are commonly presumed to initiate self-organisation. We demonstrate that a selection of simple, canonical transport models with only mild multistable non-linearities can satisfy the Turing instability conditions while also robustly exhibiting only transient patterns. Hence, a Turing-like instability is insufficient for the existence of a patterned state. While it is known that linear theory can fail to predict the formation of patterns, we demonstrate that such failures can appear robustly in systems with multiple stable homogeneous equilibria. Given that biological systems such as gene regulatory networks and spatially distributed ecosystems often exhibit a high degree of multistability and nonlinearity, this raises important questions of how to analyse prospective mechanisms for self-organisation.

A Conservative Memristive Chaotic System with Extreme Multistability and Its Application in Image Encryption.

In this work, a novel conservative memristive chaotic system is constructed based on a smooth memristor. In addition to generating multiple types of quasi-periodic trajectories within a small range of a single parameter, the amplitude of the system can be controlled by changing the initial values. Moreover, the proposed system exhibits nonlinear dynamic characteristics, involving extreme multistability behavior of isomorphic and isomeric attractors. Finally, the proposed system is implemented using STMicroelectronics 32 and applied to image encryption. The excellent encryption performance of the conservative chaotic system is proven by an average correlation coefficient of 0.0083 and an information entropy of 7.9993, which provides a reference for further research on conservative memristive chaotic systems in the field of image encryption.

Dynamical hallmarks of cancer: Phenotypic switching in melanoma and epithelial-mesenchymal plasticity.

Phenotypic plasticity was recently incorporated as a hallmark of cancer. This plasticity can manifest along many interconnected axes, such as stemness and differentiation, drug-sensitive and drug-resistant states, and between epithelial and mesenchymal cell-states. Despite growing acceptance for phenotypic plasticity as a hallmark of cancer, the dynamics of this process remains poorly understood. In particular, the knowledge necessary for a predictive understanding of how individual cancer cells and populations of cells dynamically switch their phenotypes in response to the intensity and/or duration of their current and past environmental stimuli remains far from complete. Here, we present recent investigations of phenotypic plasticity from a systems-level perspective using two exemplars: epithelial-mesenchymal plasticity in carcinomas and phenotypic switching in melanoma. We highlight how an integrated computational-experimental approach has helped unravel insights into specific dynamical hallmarks of phenotypic plasticity in different cancers to address the following questions: a) how many distinct cell-states or phenotypes exist?; b) how reversible are transitions among these cell-states, and what factors control the extent of reversibility?; and c) how might cell-cell communication be able to alter rates of cell-state switching and enable diverse patterns of phenotypic heterogeneity? Understanding these dynamic features of phenotypic plasticity may be a key component in shifting the paradigm of cancer treatment from reactionary to a more predictive, proactive approach.

Mechanical Fourier transform for programmable metamaterials.

Proactively programming materials toward target nonlinear mechanical behaviors is crucial to realize customizable functions for advanced devices and systems, which arouses persistent explorations for rapid and efficient inverse design strategies. Herein, we propose a "mechanical Fourier transform" strategy to program mechanical behaviors of materials by mimicking the concept of Fourier transform. In this strategy, an arbitrary target force-displacement curve is decomposed into multiple cosine curves and a constant curve, each of which is realized by a rationally designed multistable module in an array-structured metamaterial. Various target curves with distinct shapes can be rapidly programmed and reprogrammed through only amplitude modulation on the modules. Two exemplary metamaterials are demonstrated to validate the strategy with a macroscale prototype based on magnet lattice and a microscale prototype based on an etched silicon wafer. This strategy applies to a variety of scales, constituents, and structures, and paves a way for the property programming of materials.

Warming up recurrent neural networks to maximise reachable multistability greatly improves learning.

Training recurrent neural networks is known to be difficult when time dependencies become long. In this work, we show that most standard cells only have one stable equilibrium at initialisation, and that learning on tasks with long time dependencies generally occurs once the number of network stable equilibria increases; a property known as multistability. Multistability is often not easily attained by initially monostable networks, making learning of long time dependencies between inputs and outputs difficult. This insight leads to the design of a novel way to initialise any recurrent cell connectivity through a procedure called "warmup" to improve its capability to learn arbitrarily long time dependencies. This initialisation procedure is designed to maximise network reachable multistability, i.e., the number of equilibria within the network that can be reached through relevant input trajectories, in few gradient steps. We show on several information restitution, sequence classification, and reinforcement learning benchmarks that warming up greatly improves learning speed and performance, for multiple recurrent cells, but sometimes impedes precision. We therefore introduce a double-layer architecture initialised with a partial warmup that is shown to greatly improve learning of long time dependencies while maintaining high levels of precision. This approach provides a general framework for improving learning abilities of any recurrent cell when long time dependencies are present. We also show empirically that other initialisation and pretraining procedures from the literature implicitly foster reachable multistability of recurrent cells.

Multi-Stability of the Extensible Origami Structures.

Multi-stable structures and metamaterials with more than two stable states are widely applied in diversified engineering applications. Non-rigid foldable origami patterns have provided an effective way of designing multi-stable structures. But most of them have only two stable states and therefore require a combination of many units to achieve multi-stability. Here, a series of extensible origami structures are proposed with generic multi-stability based on non-rigid wrapping origami. Through a kinematic analysis and experiments, it is demonstrate that a sequential folding among different layers of the structures is created to generate a continuous rigid origami range and several discrete rigid origami states, which consequently leads to the multi-stability of the extensible origami structures. Moreover, the effects of design parameters on the mechanical properties of the structures are investigated by numerical simulation, enabling properties programmability upon specific needs. This study thus paves a new pathway for the development of novel multi-stable origami structures.

Theoretical and computational tools to model multistable gene regulatory networks.

The last decade has witnessed a surge of theoretical and computational models to describe the dynamics of complex gene regulatory networks, and how these interactions can give rise to multistable and heterogeneous cell populations. As the use of theoretical modeling to describe genetic and biochemical circuits becomes more widespread, theoreticians with mathematical and physical backgrounds routinely apply concepts from statistical physics, non-linear dynamics, and network theory to biological systems. This review aims at providing a clear overview of the most important methodologies applied in the field while highlighting current and future challenges. It also includes hands-on tutorials to solve and simulate some of the archetypical biological system models used in the field. Furthermore, we provide concrete examples from the existing literature for theoreticians that wish to explore this fast-developing field. Whenever possible, we highlight the similarities and differences between biochemical and regulatory networks and 'classical' systems typically studied in non-equilibrium statistical and quantum mechanics.

Temporal Mapper: Transition networks in simulated and real neural dynamics.

Characterizing large-scale dynamic organization of the brain relies on both data-driven and mechanistic modeling, which demands a low versus high level of prior knowledge and assumptions about how constituents of the brain interact. However, the conceptual translation between the two is not straightforward. The present work aims to provide a bridge between data-driven and mechanistic modeling. We conceptualize brain dynamics as a complex landscape that is continuously modulated by internal and external changes. The modulation can induce transitions between one stable brain state (attractor) to another. Here, we provide a novel method-Temporal Mapper-built upon established tools from the field of topological data analysis to retrieve the network of attractor transitions from time series data alone. For theoretical validation, we use a biophysical network model to induce transitions in a controlled manner, which provides simulated time series equipped with a ground-truth attractor transition network. Our approach reconstructs the ground-truth transition network from simulated time series data better than existing time-varying approaches. For empirical relevance, we apply our approach to fMRI data gathered during a continuous multitask experiment. We found that occupancy of the high-degree nodes and cycles of the transition network was significantly associated with subjects' behavioral performance. Taken together, we provide an important first step toward integrating data-driven and mechanistic modeling of brain dynamics.