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In the game of rock-paper-scissors with three players, this paper identifies conditions for a correlated equilibrium that differs from the mixed strategy Nash equilibrium and is evolutionarily stable. For this to occur, the correlation device attaches more probability to three-way ties and solo-winner outcomes than would result from the Nash equilibrium. The correlated equilibrium is evolutionarily stable because any mutant fares worse than a signal-following player when facing two players who follow their own correlated signals. The critical quality of the correlation device is to make this true both for potential mutants who would disobey their signal and instead choose the action which would beat the action signaled to the player, as well as for potential mutants who would deviate to the action that would be beaten by what the device signals to the player. These findings reveal how a strict correlated equilibrium can produce evolutionarily stable strategies for rock-paper-scissors with three players. [ABSTRACT FROM AUTHOR]

In order to further improve the performance of impregnated paper decorated blockboard (ecological board), high-density fiberboard (HDF) was selected as the equilibrium layer to replace the commonly used poplar veneer. Results showed that the performance of HDF ecological board can be comparable to that of poplar veneer ecological board. It had good appearance quality, and its surface scratch resistance, surface wear resistance, water resistance and mechanical properties met the requirements of National Standard GB/T 34722-2017. The surface cracking resistance of the ecological board prepared with HDF as the equilibrium layer reached the highest level (grade 5), far better than that of the poplar veneer ecological board. This was because HDF was a relatively homogeneous material, and its dry shrinkage in both the transverse direction and along the grain direction was much lower than that of the poplar veneer. This characteristic of HDF made it possible to improve the dimensional stability and bending resistance of blockboard substrates under dry and hot conditions. The formaldehyde emission of the HDF ecological board was higher than that of the poplar veneer ecological board, but it met the formaldehyde emission requirements of indoor materials according to GB 18580-2001. [ABSTRACT FROM AUTHOR]

Many methods to accelerate sampling of molecular configurations are based on the idea that temperature can be used to accelerate rare transitions. These methods typically compute equilibrium properties at a target temperature using reweighting or through Monte Carlo exchanges between replicas at higher temperatures. A recent paper [G. M. Rotskoff and E. Vanden-Eijnden, Phys. Rev. Lett. 122, 150602 (2019)] demonstrated that accurate equilibrium densities of states can also be computed through a nonequilibrium "quench" process, where sampling is performed at a higher temperature to encourage rapid mixing and then quenched to lower energy states with dissipative dynamics. Here, we provide an implementation of the quench dynamics in LAMMPS and evaluate a new formulation of nonequilibrium estimators for the computation of partition functions or free energy surfaces (FESs) of molecular systems. We show that the method is exact for a minimal model of N-independent harmonic springs and use these analytical results to develop heuristics for the amount of quenching required to obtain accurate sampling. We then test the quench approach on alanine dipeptide, where we show that it gives an FES that is accurate near the most stable configurations using the quench approach but disagrees with a reference umbrella sampling calculation in high FE regions. We then show that combining quenching with umbrella sampling allows the efficient calculation of the free energy in all regions. Moreover, by using this combined scheme, we obtain the FES across a range of temperatures at no additional cost, making it much more efficient than standard umbrella sampling if this information is required. Finally, we discuss how this approach can be extended to solute tempering and demonstrate that it is highly accurate for the case of solvated alanine dipeptide without any additional modifications. [ABSTRACT FROM AUTHOR]

The cooperative operation of cascade reservoir systems is an efficient way to regulate water resources. However, noncooperation among various reservoir stakeholders is often observed in practice; this produces an interesting dilemma in the game of water resource management. Considering the upper Yellow River cascade reservoir system as a case study, in this paper we model and analyze the cooperation dilemma in a cascade reservoir system. In our game theoretical analysis, we find that, except for the most upstream reservoir, all reservoirs have free-ride strategies. The free-ride strategy indicates that a reservoir obtains free gain from the cooperation of other reservoirs due to spatial connections, and this fact changes the cooperative game in terms of equilibrium and benefit allocation. The results show that the regulation capacity of the free rider directly affects the equilibrium and benefit allocation of the game. A midstream reservoir with a small or medium regulation capacity tends to employ a free-ride strategy. A midstream reservoir with a large regulation capacity can entirely interrupt the cooperation between upstream and downstream reservoirs, interestingly, which can lead to the disappearance of the free-ride strategy for the midstream reservoir. However, the downstream reservoir may employ a free-ride strategy when the midstream reservoir chooses to cooperate. This implies that grand cooperation is not stable when considering free-ride, whereas partial coalitions are more likely to form. In this paper, we derive equilibrium in the cooperative game of cascade reservoirs, providing theoretical interpretation of the noncooperation phenomenon in the operation of cascade reservoirs. [ABSTRACT FROM AUTHOR]

In this paper, we study Chaplain–Lolas model in three dimensional bounded domain, which describes the invasion and diffusion process of solid tumors during the vascular growth stage. Although the model has received extensive attention since it was proposed, the existence of solutions in three-dimensional space is still missing, and only a global small solution is established by Pang and Wang (Math Models Methods Appl Sci 28(11):2211–2235, 2018) with sufficiently small proliferation coefficient. As for long time behavior, there are only corresponding stability result of constant steady-state for the case without ECM remodelling (Hillen et al. in Math Models Methods Appl Sci 25(1):165–198, 2013; Tao and Winkler in SIAM J Math Anal 47:4229–4250, 2016). If the remodeling effect of ECM is considered, the relevant research is still blank. In this paper, we first pay our attention to the study of existence of global strong solution and long time behavior. We prove that when the ratio of cell proliferation coefficient to chemotactic intensity μ χ 2 is large, there exists a unique global strong solution around the equilibrium state (1, 1, 0), and the global strong solution converges exponentially to the constant equilibrium point. In fact, such a largeness restriction on μ χ 2 is actually necessary to some extent, since that the constant equilibrium point (1, 1, 0) is actually linearly unstable when such a condition is not satisfied. Subsequently, we turn our attention to the study of dynamic behavior of solutions. We introduce a time periodic external force to this system, and prove that the solution will gradually show the same periodic behavior under the action of periodic external force, and become a time periodic solution. At last, we analysis the stability and instability of equilibrium points, and discuss the influence of spatial diffusion, chemotaxis and haptotaxis effect on the stability of solutions. In particular, we find that only chemotaxis can change the stability of the solution and make the originally stable equilibrium (1, 1, 0) unstable, while the haptotactic term has no effect on the stability. [ABSTRACT FROM AUTHOR]

The paper investigates a problem concerning the equilibrium of a solid body containing a thin rigid inclusion and a crack. It is assumed that the body is hyperelastic, therefore, it is described within the framework of finite strain theory. One of the peculiarities of this problem is a global injectivity constraint, which prevents the body, the crack faces and the inclusion from both mutual and self penetration. First, the paper deals with the differential formulation of the problem. Next, we consider energy minimization, showing that the latter provides the weak formulation of the former. Finally, the existence of the weak solution is demonstrated through the use of the variational technique. This article is part of the theme issue 'Non-smooth variational problems with applications in mechanics'. [ABSTRACT FROM AUTHOR]

The suspended parallel mechanism, due to the use of gravity as a virtual rope to provide both geometric and force constraints, leads to coupled kinematics and statics of the mechanism (geometrico-static), whose under-constrained relationship makes the coupled kinematic/hydrostatic solution very challenging. In order to solve its geometrico-static problem, this paper proposes an inverse kinematic solution algorithm and conducts an experimental study on the equilibrium configuration of the end of the two-rope robot. First, the geometric constraint equations of the force system are derived from the force system equilibrium conditions. Second, motion simulation of the end of the mechanism is carried out to analyze its motion characteristics. Finally, the trajectory similarity between the motion control test and the theoretical calculation is compared. The experimental results show that the solution algorithm proposed in this paper has high accuracy and solution efficiency. [ABSTRACT FROM AUTHOR]

This paper reports the development and switching controller design of an inverted pendulum system (IPS) platform. The euler-lagrange approach is first used to model the dynamics of the IPS which takes into account the impact of friction forces during its movements. The paper then derives a switching control method to swing the pendulum rod into the neighborhood of and stabilizing it at the equilibrium point. The implemented switching controller consists of: i) a nonlinear swing up control which brings the pendulum to the vertical position and ii) a linear stabilizing control which maintains the pendulum rod to remain in a vertical position around the neighborhood of the vertical axis. The nonlinear controller is constructed using lyapunov’s method while the linear controller is designed using linear quadratic regulator (LQR) method framework. Simulation and experimental results are presented to show the effectiveness of the proposed switching controller. [ABSTRACT FROM AUTHOR]

The literature on strategic ambiguity in classical games provides generalized notions of equilibrium in which each player best responds to ambiguous or imprecise beliefs about his opponents' strategic choices. In a recent paper, strategic ambiguity has been extended to psychological games, by taking into account ambiguous hierarchies of beliefs and max–min preferences. Given that this kind of preference seems too restrictive as a general method to evaluate decisions, in this paper we extend the analysis by taking into account α -max–min preferences in which decisions are evaluated by a convex combination of the worst-case (with weight α) and the best-case (with weight 1 − α ) scenarios. We define the α -max–min psychological Nash equilibrium; an illustrative example shows that the set of equilibria is affected by the parameter α and the larger the ambiguity, the greater the effect. We also provide a result of stability of the equilibria with respect to perturbations that involve the attitudes toward ambiguity, the structure of ambiguity, and the payoff functions: converging sequences of equilibria of perturbed games converge to equilibria of the unperturbed game as the perturbation vanishes. Surprisingly, a final example shows that the existence of equilibria is not guaranteed for every value of α. [ABSTRACT FROM AUTHOR]

In multi‐agent systems, most commonly, consensus consists in all agents converging to a common equilibrium point. For nonholonomic vehicles, which move on a Cartesian plane and occupy a physical space, it is more appropriate to speak of consensus‐based formation, which implies that the vehicles are required to converge to a relative position in a given formation while, distributively, agreeing on the center of such formation and on their orientation. In this paper we solve such a problem via a smooth, time‐varying, output‐feedback control; more precisely, without velocity measurements. In addition, and this is our main contribution, the controller is designed to satisfy pre‐imposed bounds to avoid input saturation. To the best of the authors' knowledge this is the first controller that solves the consensus‐based formation problem in networks of nonholonomic vehicles via a bounded, output‐feedback controller. The paper also provides a simulation comparison between our proposal and its unbounded counterpart. [ABSTRACT FROM AUTHOR]

This work investigates a prey–predator model featuring a Holling-type II functional response, in which the fear effect of predation on the prey species, as well as prey refuge, are considered. Specifically, the model assumes that the growth rate of the prey population decreases as a result of the fear of predators. Moreover, the detection of the predator by the prey species is subject to a delay known as the fear response delay, which is incorporated into the model. The paper establishes the preliminary conditions for the solution of the delayed model, including positivity, boundedness and permanence. The paper discusses the existence and stability of equilibrium points in the model. In particular, the paper considers the discrete delay as a bifurcation parameter, demonstrating that the system undergoes Hopf bifurcation at a critical value of the delay parameter. The direction and stability of periodic solutions are determined using central manifold and normal form theory. Additionally, the global stability of the model is established at axial and positive equilibrium points. An extensive numerical simulation is presented to validate the analytical findings, including the continuation of the equilibrium branch for positive equilibrium points. [ABSTRACT FROM AUTHOR]

This paper proposes a detection method for countering strategic attacks in zero-boundary trusted networks. In a normal network, malicious nodes are only a minority; therefore, this paper employs a simple game-theoretic approach to suppress the occurrence of malicious events. Firstly, the paper introduces a behavior-based event inference method to detect malicious events, wherein nodes reference the inference results of other nodes to form composite reports. Subsequently, the paper introduces a simple game, allowing malicious nodes to choose not to falsify reports under disadvantaged scenarios, reaching a Bayesian equilibrium with normal nodes, thereby reducing the incidence of malicious events. This method demonstrates significant effectiveness in conventional networks where malicious nodes constitute a minority. [ABSTRACT FROM AUTHOR]

• Approximation for the slope of the equilibrium line in multicomponent mixtures. • Method based on the new concept of the design component. • Design component is that eliminated from the mixture in a section of the column. • Two approximate methods of estimating the slope are adequate for design work. • These simple approximations easily programmed in any spreadsheet. There is no simple definition of the slope for multicomponent systems because the vapour liquid equilibrium is represented by a surface (which lies in hyperspace for more than 3 compounds). Thus, for multicomponent systems any pseudo-binary method for estimating tray efficiencies and HETP must rely, in part, on an approximate method of estimating the slope. The objective of this paper is to present a new method of approximating the slope in multicomponent systems based on differentiation of the phase equilibrium surface with respect to the mole fraction of the design component, defined as that compound we seek to eliminate from the mixture in a particular section of the column. There is only one design compound per column section. The approach presented here can be easily applied to absorber and stripper columns, where the concept of key components is not applicable. Two analytical approximate methods of estimating the design slope are shown to be in good agreement with the rigorous calculation even in cases where the relative volatility is not constant. These simple approximations, which need nothing beyond what is readily available from any column simulation program are adequate for design and can be programmed easily in any spreadsheet. [ABSTRACT FROM AUTHOR]

The profiles of the edge of rectangular sheets of paper folded so as to join opposite edges were measured and compared with the profiles calculated with the theory of elasticity. I show how the calculation can be accomplished by using the aspect ratio of the loops as the only input parameter. [ABSTRACT FROM AUTHOR]

Compartmental models have long served as important tools in mathematical epidemiology, with their usefulness highlighted by the recent COVID-19 pandemic. However, most of the classical models fail to account for certain features of this disease and others like it, such as the ability of exposed individuals to recover without becoming infectious, or the possibility that asymptomatic individuals can indeed transmit the disease but at a lesser rate than the symptomatic. In the first part of this paper, we propose two new compartmental epidemiological models and study their equilibria, obtaining an endemic threshold theorem for the first model. In the second part of the paper, we treat the second model as an affine control system with two controls: vaccination and mitigation. We show that this system is static feedback linearizable, presents some simulations, and investigates an optimal control version of the problem. We conclude with some open problems and ideas for future research. [ABSTRACT FROM AUTHOR]

This paper studies a Bayesian persuasion game in which a receiver can receive signals from two senders. We study under what circumstances the competition between senders induces them to fully disclose all of the signals available. We find that if the senders' preferences are such that they are opposite to the same degree across states (to be made precise in the paper), full disclosure is the only equilibrium outcome of the game. Furthermore, we find that the above condition on the senders' preferences is also necessary if we require that full disclosure be the only equilibrium outcome for any receiver's utility and any information environment. [ABSTRACT FROM AUTHOR]

Modern commentators have doubts about the authenticity and cogency of the early propositions of Archimedes’ On Equilibrium of Planes Book 1. Ernst Mach famously said that the proof of Prop. 6, the so-called law of the lever, assumes what is to be proven. Comparing the initial text in Heiberg’s modern edition (1881, 1913) to the first propositions in Eutocius’ commentary on EP 1, J. L. Berggren ([1976]. ‘Spurious Theorems in Archimedes’ Equilibrium of Planes: Book I’, Archive for History of Exact Sciences 16.2 (1976), 87–103.) claimed that the propositions up through Proposition 3 of the standard modern edition are schoolbook additions written by an ancient author inferior to Archimedes. The present paper argues for the logical connectedness of Postulates 1–5 to Props. 1–6, by means of a detailed examination of the course of the argument and a re-examination of Eutocius’ remarks. The paper reinterprets the role of the empirical in the early propositions and offers a reading of the contribution of Archimedes’ mechanics to the method of EP 1. [ABSTRACT FROM AUTHOR]

Gross National Happiness (GNH), a concept first introduced by Bhutan, has gained immense traction as an alternate development paradigm to GDP toward achieving wholesome global progress. In this paper, we investigate the origins of the policy of GNH, through the theoretical lens of the punctuated equilibrium theory (PET), and when and how GNH came to the national agenda. By focusing on the year 2008, that is, when Bhutan's Government transitioned from an absolute monarchy to a democratic constitutional monarchy, this paper analyses the key events that serve as policy windows and the policy entrepreneurs responsible for agenda‐setting the policy of GNH. We argue there is a major change, such as, the government changing its form from monarchy to democracy, it is a definitive benchmark as to what punctuation means. In addition to providing a definitive meaning of "punctuation" in public policy, we also identify and discuss the key methodological issues in relation PET and offer explanations through Bhutan's policy of GNH to determine policy punctuation and measuring policy change. [ABSTRACT FROM AUTHOR]

This paper proposes a new inertial subgradient extragradient method for solving equilibrium problems with pseudomonotone and Lipschitz-type bifunctions and fixed point problems for nonexpansive mappings in real Hilbert spaces. Precisely, we prove that the sequence generated by proposed algorithm converges strongly to a common solution of equilibrium problems and fixed point problems. We use an effective self-adaptive step size rule to accelerate the convergence process of our proposed iterative algorithm. Moreover, some numerical results are given to show the effectiveness of the proposed algorithm. The results obtained in this paper extend and improve many recent ones in the literature. [ABSTRACT FROM AUTHOR]

Lotka-Volterra model continues to be of interest to numerous researchers, both in terms of its mathematical development and applications. This paper discusses an analytical solution of the Lotka-Volterra model near its equilibrium point. This solution, which is the main result of this paper, has not been previously explored by other researchers. The proposed solution is in the form of a series expansion with respect to parameter (1), representing a perturbed solution around the equilibrium point. The analytical solution is evaluated by comparing to both the corresponding exact orbit, which is directly derived from the model, and the corresponding numerical solution. Comparisons with the exact orbit reveal that the orbit formed by the analytical solution closely approximates the exact one. The orbits formed by the analytical solution are closer to the exact ones as approaches zero. Similarly, the analytical solution is also closer to the numerical solution as approaches zero. Additionally, as the solutions exhibit wave-like behavior, further observations are made regarding the 'amplitude' and 'wavelength' of the analytical solution. The wavelength and amplitude of the analytical solutions are closer to the ones of the numerical solutions as tends to zero. The amplitude and wavelength are crucial for optimizing harvesting strategies when applying the Lotka-Volterra model in integrated farming systems. [ABSTRACT FROM AUTHOR]

When starting an N -body simulation of an isolated galaxy, it is desirable to select particles from a distribution function to ensure that the model is in equilibrium. Random sampling from a DF is widely used, but results in a set of particles that differs by shot noise from that intended. This paper presents a method to reduce sampling noise that has been developed by the author in a many collaborations over a number of years. The technique has been partly described in past papers, though the ideas have not previously been gathered together, nor have its advantages been clearly demonstrated in past work. Of course, sampling errors can also be reduced by a brute force increase in the number of particles, but methods to achieve the same effect with fewer particles have obvious advantages. Here we not only describe the method, but also present three sets of simulations to illustrate the practical advantages of reducing sampling error. The improvements are not dramatic, but are clearly worth having. [ABSTRACT FROM AUTHOR]

This paper brings novel insights into group coordination and price dynamics in complex environments. We implement an overlapping-generation model in the lab, where the output dynamics is given by the well-known chaotic quadratic map. This model structure allows us to study previously unexplored parameter regions where the perfect-foresight dynamics exhibits chaotic dynamics. This paper highlights three key findings. First, the price converges to the simplest equilibria, namely the monetary steady state or the two-cycle, in all markets. Second, we document a novel and intriguing finding: we observe a non-monotonicity of the behavior when complexity increases. Convergence to the two-cycle occurs for the intermediate parameter range, while both the extreme scenarios of a simple stable two-cycle and highly non-linear dynamics (with chaos) lead to coordination on the steady state in the lab. All indicators of coordination and convergence significantly exhibit this non-monotonic relationship in the learning-to-forecast experiments and this non-monotonicity persists in the learning-to-optimize design. Third, convergence in the learning-to-optimize experiment is more challenging to achieve: coordination on the two-cycle is never observed, although the two-cycle Pareto-dominates the steady state in our design. [ABSTRACT FROM AUTHOR]

This paper considers a density-suppressed motility model with a strong Allee effect under the homogeneous Neumman boundary condition. We first establish the global existence of bounded classical solutions to a parabolic–parabolic system over an |$N $| -dimensional |$\mathbf{(N\le 3)}$| bounded domain |$\varOmega $|⁠ , as well as the global existence of bounded classical solutions to a parabolic–elliptic system over the multidimensional bounded domain |$\varOmega $| with smooth boundary. We then investigate the linear stability at the positive equilibria for the full parabolic case and parabolic–elliptic case, respectively, and find the influence of Allee effect on the local stability of the equilibria. By treating the Allee effect as a bifurcation parameter, we focus on the one-dimensional stationary problem and obtain the existence of non-constant positive steady states, which corresponds to small perturbations from the constant equilibrium |$(1,1)$|⁠. Furthermore, we present some properties through theoretical analysis on pitchfork type and turning direction of the local bifurcations. The stability results provide a stable wave mode selection mechanism for the model considered in this paper. Finally, numerical simulations are performed to demonstrate our theoretical results. [ABSTRACT FROM AUTHOR]

The behavior of a coned disk spring can be significantly affected by friction or restraint, yet the existing theoretical solutions cannot fully capture these influences. The limitation is particularly problematic for analyzing the behavior of coned disk springs with bi-stability. This paper proposes an explicit solution that can predict the behavior of the coned disk spring under these boundary conditions. The solution considers detailed influences of friction and restraint at the edges of the coned disk spring on its moment equilibrium and location of the neutral fiber. The theoretical results are validated using existing literature, FE analysis, and a series of tests. The theoretical solution confirms that the friction force at the edge of the coned spring significantly affects the axial response of the spring but not its bending moment or distribution of tangential stress. The bending moment and overall behavior of the coned disk spring are, on the other hand, very sensitive to restraints in radial directions. The proposed explicit solution shows good accuracy for coned disk springs with restrained radial stretching and rotation. The solution is particularly useful for coned disk springs in multistable structures and metamaterials. [ABSTRACT FROM AUTHOR]

The paper concerns a new iterative method for approximating a solution of an equilibrium problem involving a monotone and Lipschitz-type bifunction in a Hilbert space. Our method combines the proximal mapping with a regularization technique. When compared with known extragradient methods, the proposed method is seen to have a simpler and more elegant structure. A strong convergence theorem is established under some appropriate conditions imposed on the control parameters. Several experiments are performed in order to illustrate the numerical effectiveness of our new algorithm in comparison with that of existing methods. [ABSTRACT FROM AUTHOR]

In this paper, we propose an epidemic model of SIR type with ratio-dependent impulse control and Beddington–DeAngelis (B–D) incidence. According to the magnitude of the basic reproductive number ℛ 0 and the relation of the endemic equilibrium (S ∗ , I ∗) and the ratio threshold h , dynamical analysis of the controlled system is conducted. Under the control strategy, if ℛ 0 ≤ 1 , the solutions converge to the disease-free equilibrium. If ℛ 0 > 1 and I ∗ S ∗ > h , the impulsive system has periodic solution that is orbitally asymptotically stable, and order- k   (k > 2) periodic solution does not exist. Furthermore, if ℛ 0 > 1 and I ∗ S ∗ < h , the solution converges either to the endemic equilibrium or to a periodic solution, which is proved to be determined by the initial value. Finally, numerical simulations are performed to demonstrate the theoretical results. [ABSTRACT FROM AUTHOR]

This paper aims to study the sufficient and necessary conditions for a generalized polynomial Liénard system with a unique equilibrium and one periodic annulus. In such a case, there are two types of equilibrium: a centre or a neighbourhood of the equilibrium consisting of a hyperbolic sector and an elliptical sector. The sufficient and necessary conditions for both cases are established and global phase portraits in the Poincaré disc are presented under certain conditions. [ABSTRACT FROM AUTHOR]

In this paper, we study and characterize the nilpotent global centers of a generalized polynomial Kukles system with degree three. A sufficient and necessary condition of global centers is established under certain parametric conditions. [ABSTRACT FROM AUTHOR]

In most practical engineering applications, the translating belt wraps around two fixed wheels. The boundary conditions of the dynamic model are typically specified as simply supported or fixed boundaries. In this paper, non-homogeneous boundaries are introduced by the support wheels. Utilizing the translating belt as the mechanical prototype, the vibration characteristics of translating Timoshenko beam models with non-homogeneous boundaries are investigated for the first time. The governing equations of Timoshenko beam are deduced by employing the generalized Hamilton's principle. The effects of parameters such as the radius of wheel and the length of belt on vibration characteristics including the equilibrium deformations, critical velocities, natural frequencies, and modes, are numerically calculated and analyzed. The numerical results indicate that the beam experiences deformation characterized by varying curvatures near the wheels. The radii of the wheels play a pivotal role in determining the change in trend of the relative difference between two beam models. Comparing the results unearths that the relative difference in equilibrium deformations between the two beam models is more pronounced with smaller-sized wheels. When the two wheels are of equal size, the critical velocities of both beam models reach their respective minima. In addition, the relative difference in natural frequencies between the two beam models exhibits nonlinear variation and can easily exceed 50%. Furthermore, as the axial velocities increase, the impact of non-homogeneous boundaries on modal shape of translating beam becomes more significant. Although dealing with non-homogeneous boundaries is challenging, beam models with non-homogeneous boundaries are more sensitive to parameters, and the differences between the two types of beams undergo some interesting variations under the influence of non-homogeneous boundaries. [ABSTRACT FROM AUTHOR]

The aim of this paper is to present a new, analytical, method for computing the exact number of relative equilibria in the planar, circular, restricted 4-body problem of celestial mechanics. The new approach allows for a very efficient computer-aided proof, and opens a potential pathway to proving harder instances of the n-body problem. [ABSTRACT FROM AUTHOR]

This paper deals with numerical threshold stability of a nonlinear age-structured reaction–diffusion brucellosis model. An unconditionally positivity-preserving numerical scheme is established via a linearly implicit Euler method in time integration together with a center difference scheme in space discretization. A numerical basic reproduction number is proposed and denoted by R0Δt, which plays the same role in threshold stability analysis as the basic reproduction number of the model and converges to it as step-sizes vanishes. Namely, the numerical disease-free equilibrium is asymptotically stable if R0Δt < 1. Moreover, a unique space-independent coexistence equilibrium exists uniquely and is locally asymptotically stable while R0Δt > 1. Some numerical experiments are given in the end to confirm the efficiency of conclusions. [ABSTRACT FROM AUTHOR]

In this paper, we introduce a rehab–recovery–relapse cycle model to study the interaction between healthy individuals, individuals that might develop substance use disorders (SUD), which for simplicity here we will call susceptible individuals, individuals with SUD, and individuals recovered in a rehab community. We measure the community’s health through a system defined by four non-linear ordinary differential equations in which we include a rehab community. After computing the SUD-free and coexistence equilibrium points, we find the feasibility and stability conditions of an equivalent and reduced system obtained by nondimensionalizing the equations of the original model. We have numerically investigated the importance of the parameter values on the model’s outcome via a one- and two-strain parameter analysis. From the numerical results, we observe that an efficient rehab community can be characterized by (i) a high recovery rate (the individuals stay in that community as little time as possible) and (ii) permanent rehabilitation being preferred at the expense of a low recovery rate. [ABSTRACT FROM AUTHOR]

In this paper, we consider a diffusive predator–prey model with spatial memory of prey and gestation delay of predator. For the system without delays, we study the stability of the positive equilibrium in the case of diffusion and no diffusion, respectively. For the delayed model without diffusions, the existence of Hopf bifurcation is discussed. Further, we investigate the stability switches of the model with delays and diffusions when two delays change simultaneously by calculating the stability switching curves and obtain the existence of Hopf bifurcation. We also calculate the normal form of Hopf bifurcation to determine the direction of Hopf bifurcation and the stability of bifurcation periodic solutions. Finally, numerical simulations verify the theoretical results. [ABSTRACT FROM AUTHOR]

This paper focuses on synchronization control of the fractional-order unified chaotic system. First, the stability of equilibria is analyzed by the Routh–Hurwitz criteria. Then, three different controllers are designed to achieve chaos synchronization of the drive-response unified system. Further, the impact of the fractional order on the synchronization performance is illustrated. Numerical simulations are carried out to verify the feasibility of theoretical analysis. [ABSTRACT FROM AUTHOR]

In this paper, an enhanced equilibrium optimization (EO) version named Levy-opposition-equilibrium optimization (LOEO) is proposed to select effective features in network intrusion detection systems (IDSs). The opposition-based learning (OBL) approach is applied by this algorithm to improve the diversity of the population. Also, the Levy flight method is utilized to escape local optima. Then, the binary rendition of the algorithm called BLOEO is employed to feature selection in IDSs. One of the main challenges in IDSs is the high-dimensional feature space, with many irrelevant or redundant features. The BLOEO algorithm is designed to intelligently select the most informative subset of features. The empirical findings on NSL-KDD, UNSW-NB15, and CIC-IDS2017 datasets demonstrate the effectiveness of the BLOEO algorithm. This algorithm has an acceptable ability to effectively reduce the number of data features, maintaining a high intrusion detection accuracy of over 95%. Specifically, on the UNSW-NB15 dataset, BLOEO selected only 10.8 features on average, achieving an accuracy of 97.6% and a precision of 100%. [ABSTRACT FROM AUTHOR]

In this paper, we study a network-based SIR epidemic model with a saturated treatment function in which a parameter α is introduced to measure the extent of the effect of the infected being delayed for treatment. Our aim is to present a global analysis and to investigate how the parameter α affects the spreading of diseases. Our main results are as follows: (1) In the case of the threshold value R 0 < 1 , there exist two values of α : α c and α 0 , such that the disease-free equilibrium is globally asymptotically stable when α ≤ α c and multiple endemic equilibria exist when α ≥ α 0 . This means that the parameter α has an essential influence on the spreading of the disease. (2) In the case of the threshold value R 0 > 1 , if the model has only one endemic equilibrium, then the unique endemic equilibrium is globally attractive. In this case, it is also proved that if α ≤ α c , then the endemic equilibrium has only one, so is globally attractive. In addition, numerical simulation is performed to illustrate our theoretical results. [ABSTRACT FROM AUTHOR]

In this paper, by revisiting coderivative calculus rules for convex multifunctions in finite-dimensional spaces, we derive formulae for estimating/computing the basic subdifferential and the coderivative of the efficient point multifunction of parametric convex vector optimization problems. These results are then applied to a broad class of conventional convex vector optimization problems with the presence of operator constraints and equilibrium ones. Examples are also designed to analyze and illustrate the obtained results. [ABSTRACT FROM AUTHOR]

In this paper, the simple refined plate theory (S-RPT) is extended for the analysis of the bending and buckling behaviours of functionally graded graphene platelets reinforced composite (FG-GPLRC) plates supported by local elastic foundations under different boundaries. For the first time, an analytical method for determining the location of the local elastic foundation distribution by simple integration is extended to the analysis of the bending and buckling behaviour of plates. The method avoids complex calculations compared to previous methods for determining the position of the elastic foundation. Compared with other simplified plate theories, the displacement pattern of S-RPT is able to reflect the interrelationship between the gradient material properties and the displacement distribution along plate's thickness. The material properties of FG-GPLRC plates are affected by temperature. Using the static equilibrium method, the plate equilibrium equations are derived by directly integrating the three-dimensional elastic equations along the plate cross section. Galerkin's method is used to solve the governing equations. The accuracy of S-RPT under different boundary conditions and the accuracy of the analytical method for determining the location of the elastic foundation are verified by comparing the numerical results with the existing literature. Finally, the effects of different distribution patterns, weight fractions of GPLs, thickness ratios, aspect ratios, boundary conditions, temperature, elastic foundation distribution patterns, and elastic foundation parameters were investigated in detail. [ABSTRACT FROM AUTHOR]

The commensal symbiosis system with the Allee effect and single feedback control is proposed and analyzed in this paper. The stability analysis of all possible equilibrium points is discussed, and the sufficient conditions for global stability of the interior equilibrium points are obtained. The occurrence of transcritical bifurcation and saddle-node bifurcation around the equilibrium points is investigated. Finally, the main results of the model are illustrated by numerical simulations. [ABSTRACT FROM AUTHOR]

This paper analyzes the M/M/c queueing system with server working breakdown and impatient customers under the classical truncated retry strategy. The steady-state equilibrium conditions of the system are obtained using the matrixgeometric solution method. Then the steady-state probabilities and the performance indicators of the system in the steadystate case are obtained using the Markov process theory and Gauss-Seidel iterative algorithm. Numerical experiments are conducted to assess the system’s steady-state performance indicators. Finally, we developed an optimization model for the system and derived the optimal parameters from the analysis of the optimization function. [ABSTRACT FROM AUTHOR]

In this paper, we study the boundedness, stability, and the rate of convergence of positive solutions of the following system of difference equations: x n + 1 = α + y n - 1 x n p , y n + 1 = α + x n - 1 y n q , n = 0 , 1 , 2 ,... where parameters α , p, q ∈ (0 , + ∞) , and the initial values x i , y i are arbitrary positive numbers for i = - 1 , 0 . [ABSTRACT FROM AUTHOR]

In this paper, we present certain complete solutions in the dilatation theory of elasticity. This model can be derived as a special case of Eringen's linear theory of microstretched elastic solids when microrotations are absent. It is also a version of the theory of materials with voids. The dilatation theory can be considered the simplest theoretical model of microstructured materials and is suitable for investigating various phenomena that occur in engineering, geomechanics, and biomechanics. We establish three complete solutions to the displacement equations of equilibrium that are the counterpart of the Green–Lamé (GL), Boussinesq–Papkovich–Neuber (BPN), and Cauchy–Kowalevski–Somigliana (CKS) solutions of classical elasticity. The links between these BPN and CKS solutions are established. Then, we present a representation of the BPN solution in the case of axisymmetry. The results presented here are useful for solving axisymmetric problems in semi-infinite and infinite domains. [ABSTRACT FROM AUTHOR]

In this paper, we develop an integrodifference equation model that incorporates spatial memory and learning so that each year, a fraction of the population use the same dispersal kernel as the previous year, and the remaining individuals return to where they bred or were born. In temporally static environments, the equilibrium of the system corresponds to an ideal free dispersal strategy, which is evolutionarily stable. We prove local stability of this equilibrium in a special case, and we observe convergence towards this equilibrium in numerical computations. When there are periodic or stochastic temporal changes in the environment, the population is less able to match the environment, but is able to do so to some extent depending on the parameters. Overall, the mechanism proposed in this model shows a possible way for the dispersal kernel of a population to evolve towards an ideal free dispersal kernel. [ABSTRACT FROM AUTHOR]

Michel Serres proposes that we reform our relation to the non-human world by striking a new contract to extend democratic rights and legal protections to nature. Following Serres's lead, this has for the most part been understood in strictly legal terms. In this paper, I will show that the natural contract also has a narrative dimension, and moreover that taking this into account reveals an engagement with the Principle of Sufficient Reason that puts the relation of the natural contract with law in a new light. The natural contract appears not as a standalone, law-based response to the climate emergency but as part of an ongoing rational practice that involves the law, the sciences, and a wider narrative exploration of the human and the non-human. After outlining Serres's proposal for a natural contract, I will look briefly to his account of Lucretius in The Birth of Physics where both narrative and contract play an important part. Law is treated as a regularity arising from the connection between events, and further as a form of equilibrium modelled on the most advanced knowledge available. Serres's discussion of Leibniz's Principle of Sufficient Reason in The Natural Contract shows that the composition of such an equilibrium is both narrative and rational. [ABSTRACT FROM AUTHOR]

This paper examines the concept of equilibrium in the work of Michel Serres. It starts with analysis of Serres's philosophy of nature and, in particular, of the Lucretian cosmology he adumbrates in his 1977 text The Birth of Physics. By beginning here, we can see that his fundamental account of the material world is framed in terms of equilibrium or, rather, as a series of different equilibria that are dynamic, internally nested and reactive to each other in complex ways. In this respect, Serres's philosophy of nature resonates with work in contemporary Earth System Science that models the planet as a complex, adaptive system trending towards homeostatic regulation. But crucially, Serres goes further by extracting from this modelling important insights into human values. That is to say, he suggests that necessary and urgent questions about what sort of people we must be and what sort of social order we must pursue can be addressed through the prism of the concept of equilibrium. At the time of the Anthropocene, when planetary stability itself seems to be at stake, with potentially catastrophic implications for present and future life on earth, Serres's work thus shows itself to be timely and apposite across a range of disciplinary applications. [ABSTRACT FROM AUTHOR]

The layout optimization of wind turbines seeks to improve wind power conversion efficiency by minimizing the wake effect in wind farm. However, the existing optimization methods cannot provide a layout with high output power due to their inability to weaken the energy losses caused by the wake effect between turbines. In this paper, an equilibrium optimizer with local perturbation and adaptive escape strategies, termed adaptive equilibrium optimizer (AEO), is proposed to tackle the wind farm layout optimization problem (WFLOP). To be specific, the worst turbines in the layout are re-located to better locations to reduce wind losses by enhancing the exploitation capacity of AEO with a local perturbation strategy. Then, an adaptive escape strategy supports the particles to get out of the local optimum and to search toward more promising areas, which facilitates the adjustment of the layout to reduce the wake effect. Besides, an adaptive repair operator adaptively reconfigures infeasible layouts to augment the proportion of feasible solutions in the population; thus, AEO can sufficiently explore the layout space to optimize the output power of wind farms. Twelve prohibited area constraints, three turbine scales, and three wind farm sizes are utilized to evaluate the performance of AEO in two cases with various wind speeds and directions. The experimental results demonstrate that the AEO performs excellently in terms of efficiency, robustness, and generalization for the layout optimization of turbines with different constraints, scales, and wind farm sizes in comparison with the state-of-the-art metaheuristics and other methods reported in the literature. [ABSTRACT FROM AUTHOR]

An integrated zero-carbon power plant aggregates uncontrollable green energy, adjustable load, and storage energy resources into an entity in a grid-friendly manner. Integrated zero-carbon power plants have a strong demand response potential that needs further study. However, existing studies ignore the green value of renewable energy in power plants when participating in demand response programs. This paper proposed a mathematical model to optimize the operation of an integrated zero-carbon power plant considering the green value. A demand response mechanism is proposed for the independent system operator and the integrated zero-carbon power plants. The Stackelberg gaming process among these entities and an algorithm based on dichotomy are studied to find the demand response equilibrium. Case studies verify that the mechanism activates the potential of the integrated zero-carbon power plant to realize the load reduction target. [ABSTRACT FROM AUTHOR]

In this paper, we prove the global existence of analytical solutions to the compressible Oldroyd-B model without retardation near a nonvacuum equilibrium in Rn (n = 2, 3). Zero retardation results in zero dissipation in the velocity equation, which is the main difficulty that prevents us from obtaining the long time well-posedness of solutions. Through dedicated analysis, we find that the linearized equations of this model have damping effects, which ensure the global-in-time existence of small data solutions. However, the nonlinear quadratic terms have one more order derivative than the linear part and no good structure is discovered to overcome this derivative loss problem. So we can only build the result in the analytical energy space rather than Sobolev space with finite order derivatives. [ABSTRACT FROM AUTHOR]