Bistable systems

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...

The coexistence of obligate mutualists is often precariously close to tipping points where small environmental changes can drive catastrophic shifts in species composition. For example, microbial ecosystems can collapse by the decline of a strain that provides an essential resource on which other strains cross-feed. Here, we show that tipping points, ecosystem collapse, bistability and hysteresis arise even with very weak (non-obligate) mutualism provided the population is spatially structured. Based on numeric solutions of a metacommunity model and mean-field analyses, we demonstrate that weak mutualism lowers the minimal dispersal rate necessary to avoid stochastic extinction, while species need to overcome a mean threshold density to survive in this low dispersal rate regime...

Optical bistability has the potential to emulate the capabilities of electrical flip-flops, offering plenty of applications in optical signal processing. Conventional optical bistable devices operate by altering the susceptibility of a nonlinear medium. This method, however, often results in drawbacks such as large device size, high energy consumption, or long switching times. This work proposes an optical bistable device incorporating strong optical feedback into a Fano laser. This leads to multiple stable states and introduces a region of bistability between the inherent Fano mode and a feedback-induced Fabry-Perot mode...

Cavity optomechanics is concerned with the interaction between optical cavities and mechanical resonators. Here, we present systematic research on the dynamic behaviors of cavity optomechanical systems incorporating the influence of thermal nonlinearity. A dimensionless theoretical model was established to describe the system and numerical simulations were performed to study the dynamic behaviors. We theoretically identify the staircase effect, which can abruptly alter the system parameters when adiabatically sweeping the pump laser frequency across the optical cavity resonance and driving the mechanical resonator into oscillation...

We investigate the nonlinear dynamics of an optoelectronic oscillator that is implemented with a laser diode (LD) with time-delayed feedback. In this system, electrical-to-optical conversion is directly implemented using the direct modulation of the laser diode itself, instead of an electrooptical modulator as in conventional architectures. Moreover, we consider the cubic nonlinear saturation of the characteristic laser power-intensity (P-I) transfer function far above threshold, instead of its simplified piecewise linear counterpart...

Spin-crossover (SCO) materials exhibit remarkable potential as bistable switches in molecular devices. However, the spin transition temperatures ( T c ) of known compounds are unable to cover the entire ambient temperature spectrum, largely limiting their practical utility. This study reports an exemplary two-dimensional SCO solid solution system, [Fe III (H 0.5 L Cl ) 2 - 2 x (H 0.5 L F ) 2 x ]·H 2 O (H 0.5 L X = 5- X -2-hydroxybenzylidene-hydrazinecarbothioamide, X = F or Cl, x = 0 to 1), in which the adjacent layers are adhered via hydrogen bonding...

Tunable microwave absorbers have gained significant interest due to their capability to actively control microwaves. However, the existing architecture-change-based approach lacks flexibility, and the active-element-based approach is constrained by a narrowband operation or small dynamic modulation range. Here, a novel electrically tunable microwave absorbing device (TMAD) is demonstrated that can achieve dynamic tuning of the average reflection amplitude between -13.0 and -1.2 dB over a broadband range of 8-18 GHz enabled by reversible metal electrodeposition...

Network modeling characterizes the underlying principles of structural properties and is of vital significance for simulating dynamical processes in real world. However, bridging structure and dynamics is always challenging due to the multiple complexities in real systems. Here, through introducing the individual's activity rate and the possibility of group interaction, we propose a probabilistic activity-driven (PAD) model that could generate temporal higher-order networks with both power-law and high-clustering characteristics, which successfully links the two most critical structural features and a basic dynamical pattern in extensive complex systems...

Long transient dynamics in ecological models are characterized by extended periods in one state or regime before an eventual, and often abrupt, transition. One mechanism leading to long transient dynamics is the presence of ghost attractors, states where system dynamics slow down and the system lingers before eventually transitioning to the true attractor. This transition results solely from system dynamics rather than external factors. This paper investigates the dynamics of a classical herbivore-grazer model with the potential for ghost attractors or alternative stable states...

In ecological systems, the predator-induced fear dampens the prey's birth rate; yet, it fails to extinguish their population, as they endure and survive even under significant fear-induced costs. In this study, we unveil a modified Leslie-Gower predator-prey model by incorporating the fear of predators, cooperative hunting, and predator-taxis sensitivity. We embark upon an exploration of the positivity and boundedness of solutions, unearthing ecologically viable equilibrium points and their stability conditions governed by the model parameters...

Self-organized bistability (SOB) stands as a critical behavior for the systems delicately adjusting themselves to the brink of bistability, characterized by a first-order transition. Its essence lies in the inherent ability of the system to undergo enduring shifts between the coexisting states, achieved through the self-regulation of a controlling parameter. Recently, SOB has been established in a scale-free network as a recurrent transition to a short-living state of global synchronization. Here, we embark on a theoretical exploration that extends the boundaries of the SOB concept on a higher-order network (implicitly embedded microscopically within a simplicial complex) while considering the limitations imposed by coupling constraints...

This research paper delves into the two-dimensional discrete plant-herbivore model. In this model, herbivores are food-limited and affect the plants' density in their environment. Our analysis reveals that this system has equilibrium points of extinction, exclusion, and coexistence. We analyze the behavior of solutions near these points and prove that the extinction and exclusion equilibrium points are globally asymptotically stable in certain parameter regions. At the boundary equilibrium, we prove the existence of transcritical and period-doubling bifurcations with stable two-cycle...

Traditional mechanistic trade-offs between transmission and parasite latency period length are foundational for nearly all theory on the evolution of parasite life history strategies. Prior theoretical studies demonstrate that seasonal host activity can generate a trade-off for obligate-host killer parasites that selects for intermediate latency periods in the absence of a mechanistic trade-off between transmission and latency period lengths. Extensions of these studies predict that host seasonal patterns can lead to evolutionary bistability for obligate- host killer parasites in which two evolutionarily stable strategies, a shorter and longer latency period, are possible...

Precise control of cell division is essential for proper patterning and growth during the development of multicellular organisms. Coordination of formative divisions that generate new tissue patterns with proliferative divisions that promote growth is poorly understood. SHORTROOT (SHR) and SCARECROW (SCR) are transcription factors that are required for formative divisions in the stem cell niche of Arabidopsis roots1,2 . Here we show that levels of SHR and SCR early in the cell cycle determine the orientation of the division plane, resulting in either formative or proliferative cell division...

Stacking of two-dimensional (2D) materials has emerged as a facile strategy for realising exotic quantum states of matter and engineering electronic properties. Yet, developments beyond the proof-of-principle level are impeded by the vast size of the configuration space defined by layer combinations and stacking orders. Here we employ a density functional theory (DFT) workflow to calculate interlayer binding energies of 8451 homobilayers created by stacking 1052 different monolayers in various configurations...

Weak fault signals are often overwhelmed by strong noise or interference. The key issue in fault diagnosis is to accurately extract useful fault characteristics. Stochastic resonance is an important signal processing method that utilizes noise to enhance weak signals. In this paper, to address the issues of output saturation and imperfect optimization of potential structure models in classical bistable stochastic resonance (CBSR), we propose a piecewise asymmetric stochastic resonance system. A two-state model is used to theoretically derive the output signal-to-noise ratio (SNR) of the bistable system under harmonic excitations, which is compared with the SNR of CBSR to demonstrate the superiority of the method...

In this work, we study the effect of covalent bonding on the behavior of non-equilibrium systems with the active force acting on particles along their velocity. Self-ordering of single particles does not occur in this model. However, starting from some critical polymerization degree, the ordered state is observed. It is homogeneous and exhibits no phase separation. In the ordered state, the chains prefer a near-two-dimensional configuration and all move in one direction. Importantly, the self-ordering is obtained only at intermediate active force magnitudes...

Microresonators are micron-scale optical systems that confine light using total internal reflection. These optical systems have gained interest in the past two decades due to their compact sizes, unprecedented measurement capabilities, and widespread applications. The increasingly high finesse (or Q factor) of such resonators means that nonlinear effects are unavoidable even for low power, making them attractive for nonlinear applications, including optical comb generation and second harmonic generation. In addition, light in these nonlinear resonators may exhibit chaotic behavior across wide parameter regions...

Microplastics pose a severe threat to marine ecosystems; however, relevant mathematical modeling and analysis are lacking. This paper formulates two stoichiometric producer-grazer models to investigate the interactive effects of microplastics, nutrients, and light on population dynamics under different settings. One model incorporates optimal microplastic uptake and foraging behavior based on nutrient availability for natural settings, while the other model does not include foraging in laboratory settings. We establish the well-posedness of the models and examine their long-term behaviors...

Excitable media, ranging from bioelectric tissues and chemical oscillators to forest fires and competing populations, are nonlinear, spatially extended systems capable of spiking. Most investigations of excitable media consider situations where the amplifying and suppressing forces necessary for spiking coexist at every point in space. In this case, spikes arise due to local bistabilities, which require a fine-tuned ratio between local amplification and suppression strengths. But, in nature and engineered systems, these forces can be segregated in space, forming structures like interfaces and boundaries...