Bistable Dynamics Research Articles

Design of intelligent Bayesian regularized deep cascaded NARX neurostructure for predictive analysis of FitzHugh-Nagumo bioelectrical model in neuronal cell membrane

The electrophysiological modelling paradigm unravels the complex oscillatory and excitable behaviors inherent to neural dynamics, with the FitzHugh-Nagumo model—rooted in the reductionist abstraction of Hodgkin-Huxley formalism—providing a quintessential framework for exploring the underpinnings of action potential propagation and diverse phase plane dynamics characterizing excitable membranes. The objective of this study is to present the novel intelligent computing-based Bayesian regularized multilayered deep dual cascaded nonlinear autoregressive exogenous neurostructure to model and predict the intricate dynamics of FitzHugh-Nagumo model. The numerical treatment of the FitzHugh-Nagumo (FHN) model is handled with a modified Adams-Bashforth-Moulton predictor–corrector method for three sundry scenarios encompassing the oscillatory, excitable, and bistable dynamics. These simulated temporal sequences are arbitrarily divided into training and test sets for Deep Cascaded NARX neural networks, with backpropagated refinement using the Bayesian regularization technique (DC-NARX-BR). This novel strategy is verified across reference numerical outcomes with the help of diversified evaluation metrics including mean squared error convergence plots, error histogram analysis, error regression metrics, input-error cross-correlation, and error autocorrelation plots. Comparative analysis charts present the efficacious use of the DC-NARX intelligent computing paradigm with absolute errors ranging from 10-05 to 10-12. Predictive intelligence of the step ahead DC-NARX-BR strategy is observed for the intricate FHN model dynamics with marginal deviances from realized behavior. These diminutive errors can be comprehended by the low MSE losses in the range 10-02–10-05. Exhaustive experimentational averages validate the robustness of DC-NARX intelligent computing paradigm for the correct integration with the complex bioelectrical phenomena occurring within a neuronal cell membrane.

Exploring bistable plankton dynamics: stochastic model analysis by SSF techniques

Exploring bistable plankton dynamics: stochastic model analysis by SSF techniques

Wolbachia Invasion in Mosquitoes with Incomplete CI, Imperfect Maternal Transmission and Maturation Delay.

The mechanism of cytoplasmic incompatibility (CI) is important in the study of Wolbachia invasion in wild mosquitoes. Su et al. (Bull Math Biol 84(9):95, 2022) proposed a delay differential equation model by relating the CI effect to maturation delay. In this paper, we investigate the dynamics of this model by allowing the same density-dependent death rate and distinct density-independent death rates. Through analyzing the existence and stability of equilibria, we obtain the parameter conditions for Wolbachia successful invasion if the maternal transmission is perfect. While if the maternal transmission is imperfect, we give the ranges of parameters to ensure failure invasion, successful invasion and partially suppressing, respectively. Meanwhile, numerical simulations indicate that the system may exhibit monostable and bistable dynamics when parameters vary. Particularly, in the bistable situation an unstable separatrix, like a line, exists when choosing constant functions as initial values; and the maturation delay affects this separatrix in an interesting way.

Evaluating dynamic models for rigid-foldable origami: unveiling intricate bistable dynamics of stacked-Miura-origami structures as a case study.

Recent advances in origami science and engineering have particularly focused on the challenges of dynamics. While research has primarily focused on statics and kinematics, the need for effective and processable dynamic models has become apparent. This paper evaluates various dynamic modelling techniques for rigid-foldable origami, particularly focusing on their ability to capture nonlinear dynamic behaviours. Two primary methods, the lumped mass-spring-damper approach and the energy-based method, are examined using a bistable stacked Miura-origami (SMO) structure as a case study. Through systematic dynamic experiments, we analyse the effectiveness of these models in predicting bistable dynamic responses, including intra- and interwell oscillations, in different loading conditions. Our findings reveal that the energy-based approach, which considers the structure's inertia and utilizes dynamic experimental data for parameter identification, outperforms other models in terms of validity and accuracy. This model effectively predicts the dynamic response types, the rich and complex nonlinear characteristics and the critical frequency where interwell oscillations occur. Despite its relatively increased complexity in model derivation, it maintains computational efficiency and shows promise for broader applications in origami dynamics. By comparing model predictions with experimental results, this study enhances our understanding of origami dynamics and contributes valuable insights for future research and applications. This article is part of the theme issue 'Origami/Kirigami-inspired structures: from fundamentals to applications'.

Control, bi-stability, and preference for chaos in time-dependent vaccination campaign.

In this work, effects of constant and time-dependent vaccination rates on the Susceptible-Exposed-Infected-Recovered-Susceptible (SEIRS) seasonal model are studied. Computing the Lyapunov exponent, we show that typical complex structures, such as shrimps, emerge for given combinations of a constant vaccination rate and another model parameter. In some specific cases, the constant vaccination does not act as a chaotic suppressor and chaotic bands can exist for high levels of vaccination (e.g., >0.95). Moreover, we obtain linear and non-linear relationships between one control parameter and constant vaccination to establish a disease-free solution. We also verify that the total infected number does not change whether the dynamics is chaotic or periodic. The introduction of a time-dependent vaccine is made by the inclusion of a periodic function with a defined amplitude and frequency. For this case, we investigate the effects of different amplitudes and frequencies on chaotic attractors, yielding low, medium, and high seasonality degrees of contacts. Depending on the parameters of the time-dependent vaccination function, chaotic structures can be controlled and become periodic structures. For a given set of parameters, these structures are accessed mostly via crisis and, in some cases, via period-doubling. After that, we investigate how the time-dependent vaccine acts in bi-stable dynamics when chaotic and periodic attractors coexist. We identify that this kind of vaccination acts as a control by destroying almost all the periodic basins. We explain this by the fact that chaotic attractors exhibit more desirable characteristics for epidemics than periodic ones in a bi-stable state.

Fluid flow drives phenotypic heterogeneity in bacterial growth and adhesion on surfaces

Bacteria often thrive in surface-attached communities, where they can form biofilms affording them multiple advantages. In this sessile form, fluid flow is a key component of their environments, renewing nutrients and transporting metabolic products and signaling molecules. It also controls colonization patterns and growth rates on surfaces, through bacteria transport, attachment and detachment. However, the current understanding of bacterial growth on surfaces neglects the possibility that bacteria may modulate their division behavior as a response to flow. Here, we employed single-cell imaging in microfluidic experiments to demonstrate that attached Escherichia coli cells can enter a growth arrest state while simultaneously enhancing their adhesion underflow. Despite utilizing clonal populations, we observed a non-uniform response characterized by bistable dynamics, with co-existing subpopulations of non-dividing and actively dividing bacteria. As the proportion of non-dividing bacteria increased with the applied flow rate, it resulted in a reduction in the average growth rate of bacterial populations on flow-exposed surfaces. Dividing bacteria exhibited asymmetric attachment, whereas non-dividing counterparts adhered to the surface via both cell poles. Hence, this phenotypic diversity allows bacterial colonies to combine enhanced attachment with sustained growth, although at a reduced rate, which may be a significant advantage in fluctuating flow conditions.

Bifurcation analysis of bistable oscillator dynamics for human hair-cell bundle structures by mapping the Floquet multipliers

Bifurcation analysis of bistable oscillator dynamics for human hair-cell bundle structures by mapping the Floquet multipliers

Bistable response and quasi-periodicity excitation of the internal dynamics of soliton molecules.

Soliton molecules, a frequently observed phenomenon in most mode-locked lasers, have intriguing characteristics comparable to their matter molecule counterparts. However, there are rare explorations of the deterministic control of the underlying physics within soliton molecules. Here, we demonstrate the bistable response of intramolecular motion to external stimuli and identify a general approach to excite their quasi-periodic oscillations. By introducing frequency-swept gain modulation, the intrinsic resonance frequency of the soliton molecule is observed in the simulation model. Applying stronger modulation, the soliton molecule exhibits divergent response susceptibility to up- and down-sweeping, accompanied by a jump phenomenon. Quasi-periodic intramolecular oscillations appear at the redshifted resonance frequency. Given the leading role of bistability and quasi-periodic dynamics in nonlinear physics, our research provides insights into the complex nonlinear dynamics within dissipative soliton molecules. It may pave the way to related experimental studies on synchronization and chaos at an ultrafast time scale.

Tuning of magnetic bistability and domain wall dynamics in magnetic microwires

A unique combination of unusual magnetic properties, such as magnetic bistability associated with ultrafast domain wall propagation or ultrasoft magnetic properties, together with excellent mechanical and corrosion properties can be obtained in amorphous microwires. Such ferromagnetic microwires coated with insulating and flexible glass-coating with diameters ranging from 0.1 to 100 can be prepared using the Taylor-Ulitovsky method. Magnetic properties of glass-coated microwires are affected by chemical compositions of the metallic nucleus and can be substantially modified by post-processing. We provide an overview of the routes allowing tuning of hysteresis loops and domain wall dynamics in amorphous microwires and new experimental results on the dependence of hysteresis loops on external stimuli, such as applied stress and temperature.

A Formal Model of Affiliative Interpersonality

Capturing the complexity of interpersonal dynamics—emerging from approach and avoidance motives of two individuals in dyadic interplay—remains challenging. In line with calls for embracing complexity in psychological research using formal modeling, we employed evolutionary game theory to investigate the underlying mechanisms of affiliative interpersonality. We constructed a relational state space that represents the ways of relating available in the momentary state of an interpersonal relationship. Next, we modeled relationships as trajectories in that relational space. Qualitatively different interpersonal dynamics emerged: (a) global stability with only one relational attractor (e.g., pure reciprocal friendliness), (b) bistability with two mutually exclusive attractors (e.g., either pure friendliness or pure distance), and (c) cycles between friendliness and distance in the relational space. The bistable dynamics appear to resemble the phenomenon of interpersonal complementarity (e.g., friendliness invites friendliness). Furthermore, the model generates psychopathologically relevant dynamics (e.g., oscillating, unstable interpersonal relationships in borderline personality disorder).

Nonequilibrium statistical mechanics of money/energy exchange models

Many-body dynamical models in which Boltzmann statistics can be derived directly from the underlying dynamical laws without invoking the fundamental postulates of statistical mechanics are scarce. Interestingly, one such model is found in econophysics and in chemistry classrooms: the money game, in which players exchange money randomly in a process that resembles elastic intermolecular collisions in a gas, giving rise to the Boltzmann distribution of money owned by each player. Although this model offers a pedagogical example that demonstrates the origins of Boltzmann statistics, such demonstrations usually rely on computer simulations. In fact, a proof of the exponential steady-state distribution in this model has only become available in recent years. Here, we study this random money/energy exchange model and its extensions using a simple mean-field-type approach that examines the properties of the one-dimensional random walk performed by one of its participants. We give a simple derivation of the Boltzmann steady-state distribution in this model. Breaking the time-reversal symmetry of the game by modifying its rules results in non-Boltzmann steady-state statistics. In particular, introducing ‘unfair’ exchange rules in which a poorer player is more likely to give money to a richer player than to receive money from that richer player, results in an analytically provable Pareto-type power-law distribution of the money in the limit where the number of players is infinite, with a finite fraction of players in the ‘ground state’ (i.e. with zero money). For a finite number of players, however, the game may give rise to a bimodal distribution of money and to bistable dynamics, in which a participant’s wealth jumps between poor and rich states. The latter corresponds to a scenario where the player accumulates nearly all the available money in the game. The time evolution of a player’s wealth in this case can be thought of as a ‘chemical reaction’, where a transition between ‘reactants’ (rich state) and ‘products’ (poor state) involves crossing a large free energy barrier. We thus analyze the trajectories generated from the game using ideas from the theory of transition paths and highlight non-Markovian effects in the barrier crossing dynamics.

A social inference model of idealization and devaluation.

People often form polarized beliefs, imbuing objects (e.g., themselves or others) with unambiguously positive or negative qualities. In clinical settings, this is referred to as dichotomous thinking or "splitting" and is a feature of several psychiatric disorders. Here, we introduce a Bayesian model of splitting that parameterizes a tendency to rigidly categorize objects as either entirely "Bad" or "Good," rather than to flexibly learn dispositions along a continuous scale. Distinct from the previous descriptive theories, the model makes quantitative predictions about how dichotomous beliefs emerge and are updated in light of new information. Specifically, the model addresses how splitting is context-dependent, yet exhibits stability across time. A key model feature is that phases of devaluation and/or idealization are consolidated by rationally attributing counter-evidence to external factors. For example, when another person is idealized, their less-than-perfect behavior is attributed to unfavorable external circumstances. However, sufficient counter-evidence can trigger switches of polarity, producing bistable dynamics. We show that the model can be fitted to empirical data, to measure individual susceptibility to relational instability. For example, we find that a latent categorical belief that others are "Good" accounts for less changeable, and more certain, character impressions of benevolent as opposed to malevolent others among healthy participants. By comparison, character impressions made by participants with borderline personality disorder reveal significantly higher and more symmetric splitting. The generative framework proposed invites applications for modeling oscillatory relational and affective dynamics in psychotherapeutic contexts. (PsycInfo Database Record (c) 2024 APA, all rights reserved).

Co-feeding transmission leads to bi-stability of tick-borne disease spread dynamics

Considering that co-feeding transmission depends on the loads of infected ticks on each host, we develop a tick-borne disease dynamics model with co-feeding transmission probability peaking at an intermediate level of infected tick loads. We stratify tick and host population by their infection status and divide the vector population in terms of infection status and post-egg stages (larvae, nymphs and adults). We use the tick population dynamics and disease spread basic reproduction numbers and co-feeding transmission characteristics to describe the disease endemic structure, and show, for the first time, that density-dependent co-feeding transmission provides a novel mechanism for bi-stability. Numerical simulations based on parameters from laboratory and fields data confirm the possibility of bi-stability in biologically realistic settings, and sensitivity analyses show that the nymphal tick load value at which the co-feeding transmission probability reaches the maximum impacts most significantly on the stable endemic equilibrium value.

Magnetic Domain Wall Networked Films – Configurational Switching for Tunable Magnetization Dynamics by Perforated Thin Films

AbstractSetting the magnetization and its properties in magnetic materials and films is of the utmost fundamental and technological importance for magnetic applications and devices. Magnetic permeabilities in a material are generally defined by the acting magnetic anisotropies together with an applied magnetic field. Here, deterministic switching of the effective dynamic magnetic properties is demonstrated by tunable networks of magnetic domain walls. By perforating magnetic films, a reversible switching between different magnetization states is achieved. Due to the resulting local effective dynamic fields for the changed domain configurations, different zero‐field permeability spectra are attained for the same material structure. Using local configurational magnetic resonances confined by magnetic domain walls, deterministic switchable bimodal dynamic behavior is achieved. Dynamic magnetooptical Kerr microscopy with picosecond temporal resolution proves that the varying periodic magnetic domain configurations are responsible for the dynamic magnetic bistability. In particular, the field‐free precessional magnetic response can be reproducibly switched between 1.3 and 2.3 GHz. The magnetization dynamics can be modified by small interventions in a repeatable manner beyond fixed material and structural properties. The described fundamental mechanism enables to design new energy efficient configurational microwave devices by switching between zero‐field magnetic arrangements.

Bistability and Bifurcations of Tumor Dynamics with Immune Escape and the Chimeric Antigen Receptor T-Cell Therapy

Tumor immune escape refers to the inability of the immune system to clear tumor cells, which is one of the major obstacles in designing effective treatment schemes for cancer diseases. Although clinical studies have led to promising treatment outcomes, it is imperative to design theoretical models to investigate the long-term treatment effects. In this paper, we develop a mathematical model to study the interactions among tumor cells, immune escape tumor cells, and T lymphocyte. The chimeric antigen receptor (CAR) T-cell therapy is also described by the mathematical model. Bifurcation analysis shows that there exists backward bifurcation and saddle-node bifurcation when the immune intensity is used as the bifurcation parameter. The proposed model also exhibits bistability when its parameters are located between the saddle-node threshold and backward bifurcation threshold. Sensitivity analysis is performed to illustrate the effects of different mechanisms on the backward bifurcation threshold and basic immune reproduction number. Simulation studies confirm the bifurcation analysis results and predict various types of treatment outcomes using different CAR T-cell therapy strengths. Analysis and simulation results show that the immune intensity can be used to control the tumor size, but it has no effect on the control of the immune escape tumor size. The introduction of the CAR T-cell therapy will reduce the immune escape tumor size and the treatment effect depends on the CAR T-cell therapy strength.

Numerical and experimental study of impact dynamics of bistable buckled beams

Bistable systems have been of great research interest due to their rich dynamics arising from a variety of excitations. This study presents an investigation into the nonlinear dynamics of a continuous bistable beam subjected to a form of vibro-impact forcing. A fixed–fixed Euler–Bernoulli beam, precompressed to achieve bistability, is considered, while a shaker with sinusoidally-prescribed velocity applies transverse impact forcing. By varying excitation parameters such as frequency and amplitude, the system response can be tuned. The study begins by employing a Galerkin expansion to the continuous equation of motion, using the buckling modes to remove buckling level dependence and ensure equilibrium symmetry. A Hertzian contact law is chosen to model the collision between the shaker and the buckled beam. The rich dynamics of this system are then explored through numerical and experimental analyses. The focus lies on investigating the emergence of intrawell and interwell dynamics that arise with varying excitation frequency, amplitude, and location. Moreover, we evaluate the significance of including higher-order modes in the modeling of bistable beam dynamics, particularly near snapthrough. This research provides valuable insights into the behavior of continuous bistable structures under vibro-impact forcing, contributing to the understanding and control of such systems in engineering applications.

Mathematical modeling of drug resistance in heterogeneous cancer cell populations

Drug resistance is one of the most intractable issues associated with cancer treatment in clinical practice. Mathematical models provide an analytic framework for facilitating the understanding of resistance evolution dynamics and the design of cancer clinical trial. In this paper, we develop an elementary, compartmental mathematical model for absolute drug resistance, focusing on the effects of point mutations in genetic drivers of malignancy. A set of ordinary differential equations (ODEs) is used to describe the dynamics of competing heterogeneous cancer cell populations while taking account of pharmacokinetics. All possible equilibria and their local geometric properties are analyzed, with the result suggests that the system exhibits bistable dynamics. The existence of optimal treatment time is discussed. To identify the critical parameters which influence cellular dynamics, we also perform parameter sensitivity analysis. Finally, numerical simulations are presented to verify the feasibilities of our analytical results and to find that the pre-existence of resistant cell phenotypes contributes more than resistant mutants generated during the treatment phase.

Spontaneous Vibrations and Stochastic Resonance of Short Oligomeric Springs.

There is growing interest in molecular structures that exhibit dynamics similar to bistable mechanical systems. These structures have the potential to be used as two-state operating units for various functional purposes. Particularly intriguing are the bistable systems that display spontaneous vibrations and stochastic resonance. Previously, via molecular dynamics simulations, it was discovered that short pyridine-furan springs in water, when subjected to stretching with power loads, exhibit the bistable dynamics of a Duffing oscillator. In this study, we extend these simulations to include short pyridine-pyrrole and pyridine-furan springs in a hydrophobic solvent. Our findings demonstrate that these systems also display the bistable dynamics, accompanied by spontaneous vibrations and stochastic resonance activated by thermal noise.

Spontaneous Synchronization of Two Bistable Pyridine-Furan Nanosprings Connected by an Oligomeric Bridge.

The intensive development of nanodevices acting as two-state systems has motivated the search for nanoscale molecular structures whose long-term conformational dynamics are similar to the dynamics of bistable mechanical systems such as Euler arches and Duffing oscillators. Collective synchrony in bistable dynamics of molecular-sized systems has attracted immense attention as a potential pathway to amplify the output signals of molecular nanodevices. Recently, pyridine-furan oligomers of helical shape that are a few nanometers in size and exhibit bistable dynamics similar to a Duffing oscillator have been identified through molecular dynamics simulations. In this article, we present the case of dynamical synchronization of these bistable systems. We show that two pyridine-furan springs connected by a rigid oligomeric bridge spontaneously synchronize vibrations and stochastic resonance enhances the synchronization effect.

Bistable spiral wave dynamics in electrically excitable media.

We show that a positive feedback loop between sodium current inactivation and wave-front ramp-up speed causes a saddle-node bifurcation to result in bistable planar and spiral waves in electrically excitable media, in which both slow and fast waves are triggered by different stimulation protocols. Moreover, the two types of spiral wave conduction may interact to give rise to more complex spiral wave dynamics. The transitions between different spiral wave behaviors via saddle-node bifurcation can be a candidate mechanism for transitions widely seen in cardiac arrhythmias and neural diseases.