Search Results (40)

This paper investigates the transition behaviour and stochastic resonance phenomenon in a class of bifurcation systems with a symmetric piecewise smooth potential, induced by a control parameter, under the combined influence of multiplicative white noise, additive white noise, and a periodic force. As the control parameter increases, the symmetric piecewise smooth potential of the system evolves from tristability to bistability. To study stochastic resonance in this system, an approximate Fokker–Planck equation is first derived based on Novikov’s theorem and the Fox approximation method. Subsequently, the approximate stationary probability density of the system is obtained from the Fokker–Planck equation, revealing the occurrence of a stochastic P-bifurcation. Then, within the bistable and multistable regimes, the effects of the bifurcation parameter, multiplicative noise intensity, and additive noise intensity on the mean first passage time (MFPT) are analysed. Finally, based on the mean first passage time, the response amplitude for stochastic resonance is derived via linear response theory, and the influences of the bifurcation parameter, noise intensities, correlation time, and signal frequency on the response amplitude are examined. In the bifurcation regime, the correctness of the expressions is verified numerically. It is found that multistability reduces the mean first passage time, and stochastic resonance is further analysed using the Fokker–Planck equation. Full article

This study investigates the nonlinear dynamics that emerge from the interactions between cancer cells and immune cells within a predator–prey model, wherein cancer cell growth obeys the Gompertz law. A bifurcation analysis allows for the identification of states of dormancy, uncontrolled growth, and multistability with and without chemotherapy. In the absence of chemotherapy, a Gompertz model predicts bistability with low (dormant) and high (active) tumor levels. However, unlike models based on the logistic equation, it shows that a stable tumor-free solution does not exist, consistent with the medical understanding about the risk of remaining disease even with successful treatment. Under chemotherapy, the model demonstrates highly complex dynamics with up to four coexisting stable steady states, stable tumor levels, and chemotherapy-induced oscillations. Parameter continuation studies show that the potency of immune recruitment, rate of cell inactivation, and drug saturation are essential in characterizing transitions among these dynamical regions. The analysis indicates that the choice of growth rate plays a significant role in determining the physiological implications for therapy, suggesting a cure for a model with a logistic growth rate, but merely tumor control for a Gompertzian scenario. Moreover, these results provide insights into optimal chemotherapy dosage to prevent problems associated with bistability and to capitalize on stable dormancy. Full article

Multi-stable mechanical metamaterials based on the snap-through behavior of cosine beams have been shown to have significant potential in the field of capacity absorption due to their advantages such as reusability and structural simplicity. However, traditional multi-stable metamaterials have exhibited limitations in both energy absorption and trapping ability. Inspired by the bionic multilevel structure, a novel hierarchical multi-stable cylindrical structure (HMCS) based on cosine curved beams is proposed. We investigated the snap-through behaviors and energy absorption capacity of the HMCS. Both finite element simulation results and experimental results show that the hierarchical multi-stable structure exhibits excellent specific energy absorption and energy trapping capabilities compared to traditional multi-stable cylindrical structures (TMCSs). Furthermore, by analyzing the effect of height h and thickness t on the snap-through behavior of the structure, the key parameters determining the mono-stable or bi-stable response are identified. In addition, a gradient-based study of the structure reveals the dominant role of stiffness in the snap-through behavior of multilayer structures. This work provides insights into the application of multi-stable cylindrical structures in energy trapping and absorption and offers a new strategy for designing high-efficiency energy-absorbing metamaterials. Full article

Despite its significance, hysteresis remains underrepresented in mainstream models of plasticity. In this work, we propose a novel framework that explicitly models hysteresis in simple one- and two-neuron models. Our models capture key feedback-dependent phenomena such as bistability, multistability, periodicity, quasi-periodicity, and chaos, offering a more accurate and general representation of neural adaptation. This opens the door to new insights in computational neuroscience and neuromorphic system design. Synaptic weights change in several contexts or mechanisms including, Bienenstock–Cooper–Munro (BCM) synaptic modification, where synaptic changes depend on the level of post-synaptic activity; homeostatic plasticity, where all of a neuron synapses simultaneously scale up or down to maintain stability; metaplasticity, or plasticity of plasticity; neuromodulation, where neurotransmitters influence synaptic weights; developmental processes, where synaptic connections are actively formed, pruned and refined; disease or injury; for example, neurological conditions can induce maladaptive synaptic changes; spike-time dependent plasticity (STDP), where changes depend on the precise timing of pre- and postsynaptic spikes; and structural plasticity, where changes in dendritic spines and axonal boutons can alter synaptic strength. The ability of synapses and neurons to change in response to activity is fundamental to learning, memory formation, and cognitive adaptation. This paper presents simple continuous and discrete neuro-modules with adapting feedback synapses which in turn are subject to feedback. The dynamics of continuous periodically driven Hopfield neural networks with adapting synapses have been investigated since the 1990s in terms of periodicity and chaotic behaviors. For the first time, one- and two-neuron models are considered as parameters are varied using a feedback mechanism which more accurately represents real-world simulation, as explained earlier. It is shown that these models are history dependent. A simple discrete two-neuron model with adapting feedback synapses is analyzed in terms of stability and bifurcation diagrams are plotted as parameters are increased and decreased. This work has the potential to improve learning algorithms, increase understanding of neural memory formation, and inform neuromorphic engineering research. Full article

The stability of differential equations is one of the most important aspects to consider in dynamical system theory. Chaotic systems were classified according to stability as multi-stable systems; systems with a single stable equilibrium; bi-stable systems; and, recently, mega-stable systems. Mega-stability refers to the infinity countable nested attractors of a periodically forced non-autonomous system. Many researchers attempted to present a simple mega-stable system. In this paper, we investigated the mega-stability of periodically damped non-autonomous differential systems with the following different order cases: integer and fractional. In the case of the integer order, we generalize the mega-stable system, such that the velocity is multiplied by a trigonometrical polynomial, and we present the necessary and sufficient conditions to generated countable infinity nested attractors. In the case of the fractional order, we obtained that the fractional order of periodically damped non-autonomous differential systems has infinity countable nested unstable attractors for some orders. The mega-instability was illustrated for two examples, showing the order effect on the trajectories. In addition, and to further recent work presenting simple high dimensional mega-stable chaotic systems, we introduce a 4D mega-stable hyperchaotic system, examining chaotic and hyperchaotic behaviors through Lyapunov exponents and bifurcation diagrams. Full article

Growing demands for self-powered, low-maintenance devices—especially in sensor networks, wearables, and the Internet of Things—have intensified interest in capturing ultra-low-frequency ambient vibrations. This paper introduces a hybrid energy harvester that combines elastic buckling with magnetically induced forces, enabling programmable transitions among monostable, bistable, and multistable regimes. By tuning three key parameters—buckling amplitude, magnet spacing, and polarity offset—the system’s potential energy landscape can be selectively shaped, allowing the depth and number of potential wells to be tailored for enhanced vibrational response and broadened operating bandwidths. An energy-based modeling framework implemented via an in-house MATLAB^® R2024B code is presented to characterize how these parameters govern well depths, barrier heights, and snap-through transitions, while an inverse design approach demonstrates the practical feasibility of matching industrially relevant target force–displacement profiles within a constrained design space. Although the present work focuses on systematically mapping the static potential landscape, these insights form a crucial foundation for subsequent dynamic analyses and prototype validation, paving the way for advanced investigations into basins of attraction, chaotic transitions, and time-domain power output. The proposed architecture demonstrates modularity and tunability, holding promise for low-frequency energy harvesting, adaptive vibration isolation, and other nonlinear applications requiring reconfigurable mechanical stability. Full article

Chimera states and bump states are collective synchronization phenomena observed independently (in different parameter regions) in networks of coupled nonlinear oscillators. And while chimera states are characterized by coexistence of coherent and incoherent domains, bump states consist of alternating active and inactive domains. The idea of multistable plasticity in the network connections originates from brain dynamics where the strength of the synapses (axons) connecting the network nodes (neurons) may change dynamically in time; when reaching the steady state the network connections may be found in one of many possible values depending on various factors, such as local connectivity, influence of neighboring cells etc. The sign of the link weights is also a significant factor in the network dynamics: positive weights are characterized as excitatory connections and negative ones as inhibitory. In the present study we consider the simplest case of bistable plasticity, where the link dynamics has only two fixed points. During the system/network integration, the link weights change and as a consequence the network organizes in excitatory or inhibitory domains characterized by different synaptic strengths. We specifically explore the influence of bistable plasticity on collective synchronization states and we numerically demonstrate that the dynamics of the linking may, under special conditions, give rise to co-existence of bump-like and chimera-like states simultaneously in the network. In the case of bump and chimera co-existence, confinement effects appear: the different domains stay localized and do not travel around the network. Memory effects are also reported in the sense that the final spatial arrangement of the coupling strengths reflects some of the local properties of the initial link distribution. For the quantification of the system’s spatial and temporal features, the global and local entropy functions are employed as measures of the network organization, while the average firing rates account for the network evolution and dynamics. In particular, the spatial minima of the local entropy designate the transition points between domains of different synaptic weights in the hybrid states, while the number of minima corresponds to the number of different domains. In addition, the entropy deviations signify the presence of chimera-like or bump-like states in the network. Full article

A logic gate is typically an electronic device with a Boolean or other type of function, e.g., adding or subtracting, including or excluding according to its logical properties. They can be used in electronic, electrical, mechanical, hydraulic, and pneumatic technology. This paper presents a new method for generating logic gates based on optical systems with an emission frequency equal to that used in current telecommunications systems. It uses an erbium-doped fiber laser in its monostable operating region, in contrast to most results published in the literature, where multistable behavior is required to induce dynamic changes, and where a DC voltage signal in the laser pump current provides the control between obtaining the different logic operations. The proposed methodology facilitates the generation of the gates, since it does not require taking the optical system to critical power levels that could damage the components. It is based on using the same elements that the EDFL requires to operate. The result is a system capable of generating up to five stable and robust logic gates to disturbances validated in numerical simulation and experimental setup. This eliminates the sensitivity to the initial conditions affecting the possible logic gates generated by the system and the need to add noise to the system (as is performed in works based on stochastic logic resonance). The experimental observations confirm the numerical results and open up new aspects of using chaotic systems to generate optical logic gates without bistable states. Full article

Misunderstandings in dyadic interactions often persist despite our best efforts, particularly between native and non-native speakers, resembling a broken duet that refuses to harmonise. This paper delves into the computational mechanisms underpinning these misunderstandings through the lens of the broken Lorenz system—a continuous dynamical model. By manipulating a specific parameter regime, we induce bistability within the Lorenz equations, thereby confining trajectories to distinct attractors based on initial conditions. This mirrors the persistence of divergent interpretations that often result in misunderstandings. Our simulations reveal that differing prior beliefs between interlocutors result in misaligned generative models, leading to stable yet divergent states of understanding when exposed to the same percept. Specifically, native speakers equipped with precise (i.e., overconfident) priors expect inputs to align closely with their internal models, thus struggling with unexpected variations. Conversely, non-native speakers with imprecise (i.e., less confident) priors exhibit a greater capacity to adjust and accommodate unforeseen inputs. Our results underscore the important role of generative models in facilitating mutual understanding (i.e., establishing a shared narrative) and highlight the necessity of accounting for multistable dynamics in dyadic interactions. Full article

Ocean circulation plays an important role in the formation and occurrence of extreme climate events. The study shows that the periodic variation of ocean circulation under strong wind stress is closely related to climate oscillation. Ocean circulation is a nonlinear dynamic system, which shows complex nonlinear characteristics, so the essence behind ocean circulation has not been clearly explained. Therefore, the response and evolution of the circulation system to wind stress are studied based on the bifurcation and catastrophe theories in nonlinear dynamics. First, the quasi-geostrophic gyre equation and the normalized gravity model are introduced and developed to study ocean circulation driven by wind stress, and solved using the Galerkin method. Then, the bifurcation and catastrophe behaviors of the system governed by the low-order ocean circulation model during the change in wind stress intensity and the coexistence of multiple equilibria in the circulation system are studied in detail. The results show that saddle and unstable nodes appear in the system after a cusp catastrophe. With the change in model parameters, the unstable node becomes the unstable focus, and then the subcritical Hopf bifurcation occurs. The system forms a bistable interval when the system undergoes a catastrophe twice, and the system shows hysteresis. In addition, multiple equilibrium states are coexisting in the circulating system, and the unstable equilibrium state always changes into a stable equilibrium state through vortex movement. Therefore, there is a route for the system to induce short-term climate oscillation, that is, in the multi-stable equilibrium state of the system, the vortex oscillates after being subject to small disturbances, and then triggers climate oscillation. Full article

In this investigation, a three-dimensional (3D) axisymmetric potential well-based nonlinear piezoelectric energy harvester is proposed to increase the broadband frequency response under low-strength planar external excitation. Here, a two-dimensional (2D) planar bi-stable Duffing potential is generalized into three dimensions by utilizing axial symmetry. The resulting axisymmetric potential well has infinitely many stable equilibria and one unstable equilibria at the highest point of the potential barrier for this cantilevered oscillator. Dynamics of such a 3D piezoelectric harvester with axisymmetric multi-stability are studied under planar circular excitation motion. Bifurcations of average power harvested from the two pairs of piezoelectric patches are presented against the frequency variation. The results show the presence of several branches of large-amplitude cross-well type period-1 and subharmonic solutions. Subharmonics involved in such responses are verified from the Fourier spectra of the solutions. The identified subharmonic solutions perform interesting patterns of curvilinear oscillations, which do not cross the potential barrier through its highest point. These solutions can completely or partially avoid the climbing of the potential barrier, thereby requiring low input excitation energy for barrier crossing. The influence of excitation amplitude on the bifurcations of normalized power is also investigated. Through multiple solution branches of subharmonic solutions, producing comparable power to the period-1 branch, broadband frequency response characteristics of such a 3D axisymmetically multi-stable harvester are highlighted. Full article

This article develops a multi-stable hybrid energy harvester (MSHEH) which consists of a piezoelectric energy harvester (PEH) and an electromagnetic energy harvester (EMEH). By tuning two parameters, the MSHEH can achieve a mono-stable, bi-stable, and tri-stable state, respectively. A numerical procedure is developed to compute the EMEH’s transduction factor. The obtained result is validated experimentally. Using the equivalent magnetic 2-point dipole theory, the restoring force model of the magnetic spring is established. The obtained model is verified experimentally. The energy harvesting performances of the MSHEH under the four different configurations (linear, mono-stable, bi-stable and tri-stable) subjected to frequency sweep excitations are evaluated by simulation and validated by experiment. The comparative analysis focuses on power output, accumulated harvested energy, and effective energy-harvesting bandwidth. The optimum load resistances are investigated by Pareto front optimizations. The following key findings are obtained. When subjected to high-level frequency sweep excitation, the tri-stable configuration exhibits the widest frequency bandwidth and the highest total accumulated harvested energy. When subjected to low-level frequency sweep excitation, the bi-stable configuration is more efficient in energy harvesting. The best performance trade-off between the PEH and EMEH can be achieved by selecting the optimum load resistances properly. Full article

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. Full article

This study’s objective is an irrationally nonlinear oscillating system, whose bifurcations and consequent multi-stability under the circumstances of single potential well and double potential wells are investigated in detail to further reveal the mechanism of the transition of resonance and its utilization. First, static bifurcations of its nondimensional system are discussed. It is found that variations of two structural parameters can induce different numbers and natures of potential wells. Next, the cases of mono-potential wells and double wells are explored. The forms and stabilities of the resonant responses within each potential well and the inter-well resonant responses are discussed via different theoretical methods. The results show that the natural frequencies and trends of frequency responses in the cases of mono- and double-potential wells are totally different; as a result of the saddle-node bifurcations of resonant solutions, raising the excitation level or frequency can lead to the coexistence of bistable responses within each well and cause an inter-well periodic response. Moreover, in addition to verifying the accuracy of the theoretical prediction, numerical results considering the disturbance of initial conditions are presented to detect complicated dynamical behaviors such as jump between coexisting resonant responses, intra-well period-two responses and chaos. The results herein provide a theoretical foundation for designing and utilizing the multi-stable behaviors of irrationally nonlinear oscillators. Full article

This study proposes a discrete-time eco-genetic model of a planktonic community that includes zooplankton and two competing phytoplankton haplotypes with and without a toxicity trait. The Holling type II response function describes predator consumption. We use the Ricker model to consider density limitation and regulation. The model is analytically and numerically studied. The loss of stability of fixed points occurs via the Neimark–Sacker scenario and a cascade of period-doubling bifurcations. The model reveals bistability and multistability. Therefore, the initial conditions can determine which of the coexisting dynamic modes will be attracted. If the competition of haplotypes is weaker than their self-regulation, then the variation in the current densities of community components can shift the observed dynamics, while the evolution direction remains unchanged. The ratio of haplotype fitnesses and predator pressure generally determines the asymptotic genetic composition of phytoplankton. If competition of haplotypes is higher than their self-regulation, then the bistability of monomorphic fixed points occurs when the displacement of one haplotype by another depends on initial conditions. The presence of predators can maintain the genetic polymorphism of the prey. This system shows dynamic modes similar to experimental dynamics: oscillation with delay, long-period antiphase fluctuations, and cryptic cycles emerging due to rapid evolution. Full article