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This research work provides an exhaustive investigation of the viability of different coupled wormhole (WH) geometries with the relativistic matter configurations in the f(R,G,T) extended gravity framework. We consider a specific model in the context of f(R,G,T)-gravity for this purpose. Also, we assume a static spherically symmetric spacetime geometry and a unique distribution of matter with a set of shape functions (β(r)) for analyzing different energy conditions. In addition to this, we examined WH-models in the equilibrium scenario by employing anisotropic fluid. The corresponding results are obtained using numerical methods and then presented using different plots. In this case, f(R,G,T) gravity generates additional curvature quantities, which can be thought of as gravitational objects that maintain irregular WH-situations. Based on our findings, we conclude that in the absence of exotic matter, WH can exist in some specific regions of the parametric space using modified gravity model as f(R,G,T)=R+αR2+βGn+γGln(G)+λT. [ABSTRACT FROM AUTHOR]

For some important knots, closed-form solutions are presented for the holding forces which are needed to keep a knot in equilibrium for given pulling forces. If the holding forces become zero for finite pulling forces, the knot is self-locking and is called stable. This is only possible when, first, the friction coefficient exceeds a critical value and, second, when there is additional pressure on some knot segments sandwiched by surrounding knot segments. The number of these segments depends on the topology of the knot and is characteristic for it. The other important parameter is the total curvature of the knot. In this way, the complete frictional contact inside the knot is taken into account. The presented model can explain the available experiments. [ABSTRACT FROM AUTHOR]

In this paper, we consider a predator–prey model with Cosner type functional response and combined harvesting. First, we explore the existence and stability of the equilibria. Then using the center manifold theorem and normal form theory, we investigate codimension one and codimension two bifurcations of the model. The analysis shows that the system has a variety of bifurcation phenomena including transcritical bifurcation, saddle‐node bifurcation, Hopf bifurcation, Bogdanov–Takens bifurcation and homoclinic bifurcation. Our findings indicate that the dynamics with harvesting are significantly richer than the system without harvesting. Finally, numerical simulations are provided to support the analytical results. [ABSTRACT FROM AUTHOR]

A method for constructing a feedback that ensures the attraction of trajectories of an affine system to an equilibrium state and to a given manifold is proposed. The feedback is found in an analytical form as a solution to an auxiliary optimal control problem. Sufficient conditions for the existence of the optimal control are given. Application of the proposed method to some classes of linear and nonlinear systems is discussed. [ABSTRACT FROM AUTHOR]

A general treatment function with an epidemic model that involves the delay in the treatment period has been proposed and studied in this work. This model contains two compartments, namely susceptible denoted by S(t) and infected denoted by I(t). The existence of all the fixed points has been determined. The system has two equilibrium points, namely the uninfected equilibrium point (UIEP) and the endemic equilibrium point (EEP). The conditions for local stability and Hopf bifurcation have been discussed. The stability of the periodic solutions and the direction of the Hopf bifurcation properties have been studied analytically and numerically. [ABSTRACT FROM AUTHOR]

In biology, economics, sociology as well as other fields, there is often a 2×2×2 asymmetric evolutionary game problem in which each party has a set of strategies, and different strategy combinations correspond to the specific pay-offs of each party. Since each participant dynamically adjusts the strategy for maximizing their own interests, the pay-off matrix plays an important role in the evolution of the game system. Based on the pay-off matrix, we probe into the resulting state of 2×2×2 asymmetric evolutionary games. The results show that from the information of the pay-off matrix, the judgement conditions for the system to evolve into three pure strategies, two pure strategies and one pure strategy can be determined directly. What is more, under a certain type of fixed pay-off matrix, the strategy combinations observed at different evolution times is always varying. Here, we explore the connection between the pay-off matrix and the evolution of behaviours through stability theory, and results obtained are conducive to deeply understand and predict the dynamic evolution of behaviour in game systems. [ABSTRACT FROM AUTHOR]

We consider a non-Newtonian incompressible heat conducting fluid with a prescribed nonuniform temperature on the boundary and with the no-slip boundary condition for the velocity. We assume no external body forces. For the power-law like models with the power law index bigger than or equal to 11/5 in three dimensions, we identify a class of solutions fulfilling the entropy equality and converging to the equilibria exponentially in a proper metric. In fact, we show the existence of a Lyapunov functional for the problem. Consequently, the steady solution is nonlinearly stable and attracts all proper weak solutions. [ABSTRACT FROM AUTHOR]

Generalized mass-action systems are power-law dynamical systems arising from chemical reaction networks. Essentially, every nonnegative ODE model used in chemistry and biology (for example, in ecology and epidemiology) and even in economics and engineering can be written in this form. Previous results have focused on existence and uniqueness of special steady states (complex-balanced equilibria) for all rate constants, thereby ruling out multiple (special) steady states. Recently, necessary conditions for linear stability have been obtained. In this work, we provide sufficient conditions for the linear stability of complex-balanced equilibria for all rate constants (and also for the nonexistence of other steady states). In particular, via sign vector conditions (on the stoichiometric coefficients and kinetic orders), we guarantee that the Jacobian matrix is a P-matrix. Technically, we use a new decomposition of the graph Laplacian which allows us to consider orders of (generalized) monomials. Alternatively, we use cycle decomposition which allows a linear parametrization of all Jacobian matrices. In any case, we guarantee stability without explicit computation of steady states. We illustrate our results in examples from chemistry and biology: generalized Lotka--Volterra systems and SIR models, a two-component signaling system, and an enzymatic futile cycle. [ABSTRACT FROM AUTHOR]

Threats to the stability of liberal democracies are of obvious contemporary import. Concern with stability runs through John Rawls's work. The stability that concerned him was that of fundamental terms of cooperation. Rawls long believed that the terms which would be stable were his two principles, but he eventually conceded that even a well-ordered society was more likely to be characterized by "justice pluralism" than by consensus on his own conception of justice. Contemporary liberal democracies, too, are divided about what justice demands. I believe Rawls's treatment of stability can help us understand the conditions under which fundamental terms of cooperation can be stable under non-ideal conditions such as ours. But because Rawls never worked through the consequences of his concession, his view needs to be developed before we can draw on it. Rawls's treatment makes use of elementary game theory. Thus in Theory of Justice he said -- and in Political Liberalism he implied -- that stability would result from citizens with a sense of justice "playing" strategies which combined for what was, in effect, a Nash equilibrium. I argue that his concession requires a new conception of stability and implies that Rawls cannot appeal to a Nash equilibrium to show how stability would be maintained. His concession therefore forces open a troubling gap in his analysis. I fill that gap by proposing a weaker equilibrium concept that serves Rawlsian purposes. I conclude with what this project suggests for challenges facing the fragile liberal democracies of our own time. [ABSTRACT FROM AUTHOR]

This article examines and proposes a dietary chain model with a prey shelter and alternative food sources. It is anticipated that mid-predators' availability is positively correlated with the number of refuges. The solution's existence and exclusivity are examined. It is established that the solution is bounded. It is explored whether all potential equilibrium points exist and are locally stable. The Lyapunov approach is used to investigate the equilibrium points' worldwide stability. Utilizing a Sotomayor theorem application, local bifurcation is studied. Numerical simulation is used to better comprehend the dynamics of the model and define the control set of parameters. [ABSTRACT FROM AUTHOR]

The general three-body problem is investigated with the addition of a fixed external force applied to one of the masses. It is firstly demonstrated that the centre-of-mass of the three-body system accelerates. Then, it is demonstrated that only a single, unstable, collinear equilibrium solution exits in the accelerating frame. While unstable, it is also demonstrated that this single equilibrium configuration is in principle controllable using additional control accelerations distributed between the masses. Potential applications of such an accelerated collinear equilibrium configuration are discussed for the active manoeuvring of chains of small asteroids for space resource utilisation. [ABSTRACT FROM AUTHOR]

A nonlinear dynamical model is developed in this paper that depicts interactions among vultures, human, animals and their carcasses. Diseases such as plague, anthrax and rabies are spreading due to the cascade impact caused by the catastrophic drop in the vulture population, particularly in Africa and Asia. The built model is theoretically studied using qualitative differential-equation theory to demonstrate the system’s rich dynamical features, which are critical for maintaining the ecosystem’s equilibrium. According to the qualitative findings, depending on the parameter combinations, the system not only displays stability of many equilibrium states but also experiences transcritical and Hopf bifurcations. By keeping an eye on the variables causing the decline of the vulture population, the model’s outputs may assist in maintaining balance with the prevention of the spread of disease through carcasses. Hopf-bifurcation results in the bifurcation of the limit cycle through the threshold, supporting the idea that interactions between humans and vultures may also be periodic. [ABSTRACT FROM AUTHOR]

This paper develops the methodology for modeling decision processes in complex controlled dynamic systems. The idea of balancing such systems (driving them to equilibrium) is implemented, and a new mechanism for the equilibria's stability is proposed. Such an approach involves economic–mathematical modeling jointly with systems analysis methods, economics, law, sociology, game theory, management, and performance measurement. A linear-quadratic positional differential game of several players is considered. Coefficient criteria under which the game has an equilibrium in sanctions and countersanctions and, simultaneously, no Nash equilibrium are derived. The economic and legal model of active equilibrium is studied through the legal concept of sanctions, which enlarges the practical application of this class of problems. [ABSTRACT FROM AUTHOR]

We consider a classical (capillary) model for a one-phase liquid in equilibrium. The liquid (e.g., water) is subject to a volume constraint, it does not mix with the surrounding vapour (e.g., air), it may come into contact with solid supports (e.g., a container), and it is subject to the action of an analytic potential field (e.g., gravity). The region occupied by the liquid is described as a set of locally finite perimeter (Caccioppoli set) in R³; no a priori regularity assumption is made on its boundary. The (twofold) scope in this note is to propose a weakest possible set of mathematical assumptions that sensibly describe a condition of stable equilibrium for the liquid-vapour interface (the capillary surface), and to infer from those that this interface is a smoothly embedded analytic surface. (The liquid-solid-vapour junction, or free boundary, can be present but is not analysed here.) The result relies fundamentally on the recent varifold regularity theory developed by the author and Wickramasekera, and on the identification of a suitable formulation of the stability condition. [ABSTRACT FROM AUTHOR]

We study the dynamics of an infinitesimal mass under the gravitational attraction of N - 1 primaries arranged in a planar ring configuration plus the influence of the central mass with a Manev potential (-1/r +e/r²), e ≠ 0, where e is a parameter related to the oblaticity or radiation source (according to the sign of the parameter e). Specifically, we investigate the relative equilibria of the infinitesimal mass and their linear stability as functions of the parameter e and the mass parameter \beta, the ratio of mass of the central body to the mass of one of the N - 1 remaining bodies. We also prove the nonexistence of binary collisions between the central body and the infinitesimal mass. [ABSTRACT FROM AUTHOR]

In this paper, sufficient conditions of stability for the critical equilibrium of Euler struts with three typical rigid boundaries, that is, one end fixed and the other clamped in rotation, fixed-free, pinned-pinned, are studied. A construction of a double orthonormal Fourier series for angle is presented for the three struts, respectively. By the double orthonormal series, the second variation of potential energy can be expressed in a diagonal quadratic form. The second variation of potential energy is proved to be semi-positive-definite. Sum of higher order variations than the second-order variation of potential energy is identically positive. The critical equilibrium is stable to disturbance with finite value, which is called "stable in the large" in the sense of Lagrange-Dirichlet stability criterion. Stability to disturbance with finite value includes the stability to disturbance with infinitesimal value in Koiter's theory. In addition, there is a constraint on the angle for the pinned-pinned strut, which is not included in Koiter's theory. [ABSTRACT FROM AUTHOR]

In this work, we examine a predator–prey model that considers the implicit marine reserve in prey species and a linear function of critical biomass level. The model's basic properties (existence, uniqueness, positivity, boundedness, and permanence) and equilibrium points are determined. We obtain three equilibrium points: the trivial equilibrium point, the equilibrium point where there is no harvest, and the co-existing equilibrium point. The local and global stability of each equilibrium point of the model is explored. Moreover, the interior equilibrium point is always globally asymptotically stable, and the system experiences no limit cycles around the interior equilibrium point. Numerical simulations are conducted to illustrate the theoretical results obtained. Finally, we find overlapping conditions regarding the dynamics between the model we developed and a model that considers a constant critical biomass level for certain parameters. [ABSTRACT FROM AUTHOR]

We consider the (1 + 4) -body problem with a Newtonian potential augmented by a " J 2 " inverse-cubic perturbation. We describe the square-shaped homographic motions, and we find a saddle-centre bifurcation of the rotating equilibria (RE). Further, we prove that for a sufficiently small perturbation, all square-shaped RE are unstable. [ABSTRACT FROM AUTHOR]

As the main methods of the coronavirus disease (COVID-19) transmission are air and physical contact, actions to mitigate and suppress its spread must be developed in order to change population dynamics and provide efficient control strategies. Here, these actions are described as a simple heuristic framework to establish public policies. Two control systems were studied: the first organized in the form of an algorithm stratified into three levels and the second as a minimization problem similar to optimal control strategies, applied to both social distancing and vaccination. The possible effects of these actions are modeled and applied to an extension of the Susceptible - Infected - Removed (SIR) compartmental model. The control system is developed, which is organized in the form of an algorithm stratified into three levels. These levels intend to represent social distancing strategies implemented by sanitary authorities around the globe, representing stronger or weaker grades of isolation intensity according to the ability of the healthcare system to cope with symptomatic individuals. The algorithm control is applied in a simulation, and the results give evidence of the effectiveness of the procedures adopted against the coronavirus. The model dynamics are analyzed and validated with simulations considering parameters obtained from epidemiological data from Brazil and Uruguay and in a more detailed way for three Brazilian states: São Paulo, Minas Gerais and Rio de Janeiro. The model was validated using cumulative data on cases and deaths. For cases of death, the results were satisfactory, while for case data, the response was reasonable, considering the possibility of adding delays or variations in parameters in the model. In addition, the effective reproduction number was proposed for the cities studied in Brazil, the result being relevant because it has a qualitative behavior similar to that published by official centers. This paper also discusses the implementation and optimization of social distancing and vaccination control strategies, considering different parameters and their effects on reducing the number of cases and deaths. Model simulations present promising results for developing strategies to attack COVID-19 dissemination. [ABSTRACT FROM AUTHOR]

This article studies the stability problem of a class of stochastic neutral-type inertial delay neural networks. By introducing appropriate variable transformations, the second-order differential system is transformed into a first-order differential system. Using homeomorphism mapping, standard stochastic analyzing technology, the Lyapunov functional method and the properties of a neutral operator, we establish new sufficient criteria for the unique existence and stochastically globally asymptotic stability of equilibrium points. An example is also provided, to show the validity of the established results. From our results, we find that, under appropriate conditions, random disturbances have no significant impact on the existence, stability, and symmetry of network systems. [ABSTRACT FROM AUTHOR]

In this paper, we focus on a patch-structured Nicholson's blowflies system incorporating mature delay and feedback delay. First, by exploiting the differential inequality technique, fluctuation lemma and Brouwer fixed point theorem, we obtain the persistence and existence of the positive equilibrium point with different components. Second, we develop an approach to establish some new criteria to guarantee the local stability and global attractivity of the positive equilibrium point vector, which complement and improve some existing results. Last, the effectiveness and feasibility of the theoretical results are illustrated by some computer simulations. [ABSTRACT FROM AUTHOR]

In this paper, we deal with the following chemotaxis-haptotaxis system modeling cancer invasion with nonlinear diffusion { u t = Δ u m − χ ∇ ⋅ (u ∇ v) − ξ ∇ ⋅ (u ∇ ω) + μ u (1 − u − ω) , in Ω × ℝ + , v t − Δ v + v = u , in Ω × ℝ + , ω t = − v ω , in Ω × ℝ + , where Ω ⊂ ℝN is a bounded domain. We first supplement the results of global existence and uniform boundedness of solutions for the case m = 2 N N + 2 . Then for any m > 0 and any spatial dimension, we consider the stability of equilibrium, and find that the chemotaxis has a destabilizing effect, that is for the ODEs, or the diffusion-ODE system without chemotaxis, the solutions tend to a linearly stable uniform steady state (1, 1, 0). When the chemotactic coefficient χ is large, the equilibrium (1, 1, 0) become unstable. Then we study the existence of nontrivial stationary solutions via bifurcation techniques with χ being the bifurcation parameter, and obtain nonhomogeneous patterns. At last, we also investigate the stability of these bifurcation solutions. [ABSTRACT FROM AUTHOR]

A mathematical model considering two strains of hepatitis B virus (HBV) chronic carriers, to assess the impact of dose-structured imperfect vaccine, in a population, is designed and analyzed. The model is shown to have a locally and globally asymptotically stable disease-free equilibrium (DFE) whenever its associated reproduction number is numerically less than unity. Numerical analysis of the model shows that with the expected 50% minimum efficacy of the first vaccine dose, vaccinating 55% of the susceptible population with the first vaccine dose will be sufficient to effectively control the spread of hepatitis B infection. Such effective control can also be achieved if 50% of the first vaccine dose recipients take the second dose. Threshold analysis reveals that an imperfect HBV vaccine should have positive or negative population-level effect. Latin hypercube sampling–PRCC analysis illustrates that disease transmission rate, birth rate, natural death rate and proportion of children born with maternal immunity are most influential parameters in the disease dynamics. In this paper, the sensitivity analysis based on mathematical and in addition statistical techniques have been performed to determine the significance of the model parameters. It is observed that a number of the parameters play an important role to determine the magnitude of the basic reproduction number. Sensitivity analysis is achieved to determine model parameters' importance in disease dynamics. It is observed that the reproduction number is the most responsive quantity to the potent transmission rate of HBV and in addition also vital to control the spread of the disease. [ABSTRACT FROM AUTHOR]

We state and prove a condition for the local stability of a certain class of two dimensional system of polynomial differential equations. We give some examples of polynomial differential systems of equations to demonstrate that this local stability condition established for the trivial equilibrium point (0, 0) is quite sharp and compare our result with the well known Lyapunov local stability criterion (Lyapunov's second method). [ABSTRACT FROM AUTHOR]

In this paper, the effects of prey’s fear on the dynamics of the prey, predator, and scavenger system incorporating a prey refuge with the linear type of functional response are studied theoretically as well as numerically approach. The local and global stabilities of all possible equilibrium points are investigated. The persistence conditions of the model are established. The local bifurcation analysis around the equilibrium points, as well as the Hopf bifurcation near the positive equilibrium point, are discussed and analyzed. Finally, numerical simulations are carried out, and the obtained trajectories are drowned using the application of Matlab version (6) to explain our found analytical results. [ABSTRACT FROM AUTHOR]

In this paper, we study the stability problem and large‐time behavior for the 3D Boussinesq equations with mixed partial kinematic viscosity and thermal diffusivity near one equilibrium, i.e., (U(0),Θ(0))=((0,0,0),βx3)$$ \left({U}^{(0)},{\Theta}^{(0)}\right)=\left(\left(0,0,0\right),\beta {x}_3\right) $$ with β=1$$ \beta =1 $$ (where β$$ \beta $$ is chosen to be large, e.g., satisfying the well‐known Miles‐Howard criterion). These problems can be extremely difficult due to the equations lack of full dissipation. Our results are twofold. In the first place, we establish the global H2$$ {H}^2 $$ and H3$$ {H}^3 $$ stability for the nonlinear system with seven different partially dissipated systems of Boussinesq equations. In the second place, we derive precise large‐time behavior for the linearized system. [ABSTRACT FROM AUTHOR]

We investigate the stability of equilibrium-induced optimal values with respect to reward functions f and transition kernels Q for time-inconsistent stopping problems under nonexponential discounting in discrete time. First, with locally uniform convergence of f and Q equipped with total variation distance, we show that the optimal value is semicontinuous with respect to (f,Q). We provide examples showing that continuity may fail in general, and the convergence for Q in total variation cannot be replaced by weak convergence. Next we show that, with the uniform convergence of f and Q, the optimal value is continuous with respect to (f,Q) when we consider a relaxed limit over ε-equilibria. We also provide an example showing that for such continuity the uniform convergence of (f,Q) cannot be replaced by locally uniform convergence. [ABSTRACT FROM AUTHOR]

The objective of this work was to investigate the dynamics of host–parasitoid model with spatial refuge effect. For this, two discrete host–parasitoid models were considered under spatial refuge effect. Suppose that a constant population of hosts may seek refuge and protection from an attack of parasitoids. We found the parametric factors affecting the existence of the equilibrium points and uniqueness of equilibrium points. A local stability analysis of host–parasitoid models was also carried out. Bifurcation theory was used to observe that the host–parasitoid models undergo Neimark–Sacker bifurcation. The effect of the existence of constant refuge effect on the local stability and bifurcation of models was also explored. Hybrid chaos control methodology was used to control the chaotic behavior of model. In addition, numerical simulations, bifurcation diagrams, and phase portraits of the models are also presented. [ABSTRACT FROM AUTHOR]

The phenomenon brake squeal has been an ongoing topic for decades, both in the automotive industry and in science. Although there is agreement on the excitation mechanism of brake squeal, namely self‐excitation due to frictional forces between the disk and the pad, in the subject of squeal it is very complex to discover all relevant effects and to take them into account. Several of these problems are related to nonlinearities, for example, in the contact between pad and disk or drum or in the behavior of the brake pad material. One of these nonlinear effects, which has been almost completely neglected so far, is that the brake can engage, mainly due to the bushing and joint elements within the brake, different equilibrium positions. This in fact has serious influence on the noise behavior as shown in experimental studies. For example, it is observed in experiments that, despite identical operating parameters, squeal sometimes occurs and sometimes not. In initial experimental studies, this could be related to the engaged equilibrium position. Following these experimental studies, the present paper introduces a minimal model by extending the well‐known minimal model by Hoffmann et al. by corresponding elements and nonlinearities allowing the system to engage different equilibrium positions. As will be presented, the stability behavior strongly depends on the engaged equilibrium position. Therefore, the minimal model represents the key experimentally observed issues. Additionally, a limit cycle behavior can also be observed. [ABSTRACT FROM AUTHOR]

In the present work, we employ the modified elliptic restricted three-body problem by considering some additional perturbed forces such as: the radiation pressure, the primaries' oblateness, and the effect of dust belt for studying the dynamical motion of the infinitesimal body. The semi-analytical solutions for the locations of non-collinear equilibrium points are obtained. The proposed model is applied to real astronomical systems. Thus, the Sun–Mars and the Proxima Centauri systems are used to estimate numerically and graphically the locations of these points in both systems at different values of perturbation parameters. In this context, the critical mass values are evaluated for both systems to analyze the stability motion of the infinitesimal body around the locations of equilibrium points and find the stability range of these locations. We demonstrate that the stability of non-collinear points in both systems depends on the parameter of mass ratio values of its own system. It is observed that the locations of these points and their stability will be affected significantly due to the changes in the values of perturbation parameters. • The perturbed elliptical restricted three-body problem. • The semi-analytical solutions for the locations of non-collinear equilibrium points. • The locations of non-collinear equilibrium points for Sun–Mars and Proxima Centauri systems. • The estimation of critical mass values for Sun–Mars and Proxima Centauri systems. • The stability analysis of the infinitesimal body motion around the locations of non-collinear equilibrium points. [ABSTRACT FROM AUTHOR]

This paper investigates the stability of a fully parabolic–parabolic-fluid (PP-fluid) system of the Keller–Segel–Navier–Stokes type in a bounded planar domain under the natural volume-filling hypothesis. In the limit of fast signal diffusion, we first show that the global classical solutions of the PP-fluid system will converge to the solution of the corresponding parabolic–elliptic-fluid (PE-fluid) system. As a by-product, we obtain the global well-posedness of the PE-fluid system for general large initial data. We also establish some new exponential time decay estimates for suitable small initial cell mass, which in particular ensure an improvement of convergence rate on time. To further explore the stability property, we carry out three numerical examples of different types: the nontrivial and trivial equilibriums, and the rotating aggregation. The simulation results illustrate the possibility to achieve the optimal convergence and show the vanishment of the deviation between the PP-fluid system and PE-fluid system for the equilibriums and the drastic fluctuation of error for the rotating solution. [ABSTRACT FROM AUTHOR]

Assessment of fish stocks is especially important to avoid overfishing and obtain sustainable fishing policies, and there are many stock assessment methods such as XSA, VPA, BMS, CMSY, and MSVPA to analyze fish stocks. However, these assessment methods require an important amount of data for fish stocks such as diet data, natural mortality, fishing mortality, abundance index of species, predator ratio estimates, and so on. Unfortunately, we do not have such data for most of the fish stocks, and obtaining such data requires an important amount of money and time, but we still can predict important information about fish stocks such as biomass of fish stocks, the maximum sustainable yield, the biomass of fish lost or gained due to predator-prey relations, and even can track the effect of harvesting on predator-prey relations by building a mathematical model for fish populations and implementing a stability analysis. To obtain these outputs, we only need landing data and implement a parameter estimation constrained on stability conditions derived from the stability analysis of the mathematical model. Shortly, this study shows us how important stability analysis is to obtain important information about fish populations in the absence of important data. [ABSTRACT FROM AUTHOR]

This article exposes an analysis of the membranes’ equilibrium states at sealing means for glass made canning containers through the study of energy transformations that provide control of the vacuum depth in the container under a given product processing mode. This research object is glass container packaging. The metal membranes are subject of this research. Instrumental methods were used to determine the membranes’ geometric parameters. Existing forms of membrane’ equilibrium were studied by means of mathematical modeling using energy and computational methods. While the external load changing, the membrane can change its state of stable equilibrium. As a result of study carried out, it was established that after the transition to the state of stability loss, the corresponding deflection of the membrane is more than three times less than its initial deflection. Therefore, the deformation at the loss of membrane stability never leads to a symmetrical deformation of its working cone. The set parameters of deflection contribute to the membrane’s function of controlling the vacuum depth in the container and are consistent with the set opposing pressure in the autoclave during the canned products heat treatment. The membrane potential energy is reflected by the sum of the internal and external local influences’ energies. At the issue of solving the general membrane energy equation, there was obtained the calculation equation of the membrane potential energy. The obtained equation adequacy to the operation of a real membrane at a canned food container under the action of load was verified. The result verification was carried out by substituting the experimentally obtained value of the additional deflection after the stability loss into the membrane potential energy calculation equation. A comparison of the estimated value of the pressure of the membranes stability loss with the value declared by the container lids manufacturer showed their closeness. Some difference between the declared value of the stability loss pressure and the calculated one is explained by the different hardness of tin used for making lids. The calculated equation of the membrane total energy was obtained. It is established that this resulting equation is adequate for the operation of real canning container membranes. [ABSTRACT FROM AUTHOR]

We consider families of systems of two-dimensional ordinary differential equations with the origin 0 as a non-hyperbolic equilibrium. For any number s ∈ (− ∞ , + ∞) , we show that it is possible to choose a parameter in these equations such that the stability index σ (0) is precisely σ (0) = s. In contrast to that, for a hyperbolic equilibrium x it is known that either σ (x) = − ∞ or σ (x) = + ∞. Furthermore, we discuss a system with an equilibrium that is locally unstable but globally attracting, highlighting some subtle differences between the local and non-local stability indices. [ABSTRACT FROM AUTHOR]

In this paper, we investigate a delayed predator–prey model with a prey refuge where the predator population eats the prey according to the Beddington–DeAngelis type functional response. Firstly, we consider the existence of equilibrium points. By analyzing the corresponding characteristic equations, the local stability of the trivial equilibrium, the predator–extinction balance, and the coexistence equilibrium of the system are discussed, and the existence of Hopf bifurcations concerning both delays at the coexistence equilibrium are established. Then, in accordance with the standard form method and center manifold theorem, the explicit formulas which determine the direction of Hopf bifurcation and stability of bifurcating period solutions are derived. Finally, representative numerical simulations are performed to validate the theoretical analysis. [ABSTRACT FROM AUTHOR]

In a non-negative profit game that possesses a Population Monotonic Allocation Scheme (PMAS), being a member of a larger coalition implies that your profit cannot decrease. In this paper, we refer to such games as PMAS profit games. As population monotonicity is a nice and desirable property that encourages formation of larger coalitions and implies stability of the grand coalition, we explore if this special feature of PMAS games can help in identifying additional stable coalition structures under different stability concepts in cooperative games—namely, core partitions, the von Neumann–Morgenstern (vNM) stable set, the largest consistent set, and the equilibrium process of coalition formation (EPCF)—and in developing relationships between coalition structures that are stable under these different stability concepts. We first define two special classes of players for PMAS profit games—extreme and strong players—and use them to develop an algorithm for construction of stable (core) partitions. We also use extreme players to identify absorbing states for equilibrium processes of coalition formation with high level of farsightedness. We then explore the impact of population monotonicity on the relationship between stable coalition structures under abovementioned stability concepts. While we are able to obtain some results related to stability of the grand coalition and to establish relationships between stable coalition structures under different stability notions that are consistent with the existing body of knowledge, population monotonicity in general does not add enough for strengthening of the existing results. However, we are able to show a couple of more general result that hold for arbitrary cooperative TU profit games. That is, we show that the members of vNM farsighted stable sets are core partitions, and that core partitions are members of a vNM stable sets. Moreover, we show that the members of vNM farsighted stable sets are EPCF-stable partitions. [ABSTRACT FROM AUTHOR]

In this paper we observed the global dynamics and the occurrence of a certain bifurcation for the corresponding values of a certain rational difference equation of the second order with analyzed quadratic terms. The analysis of the local stability of the unique equilibrium point, as well as the unique periodic solution of period two, was performed in detail. The constraint of the equations on both sides for the corresponding values of the parameters is proved and on this basis the global stability is analyzed. The existence of Neimark-Sacker bifurcation with respect to the arrangement of equilibrium points has been proven. Thus, the basins of attraction have been determined in full for all the positive values of the parameters and all the positive initial conditions. [ABSTRACT FROM AUTHOR]

This research manifesto has a comprehensive discussion of the global dynamics of an achievable discrete-time two predators and one prey Lotka–Volterra model in three dimensions, i.e., in the space R 3 . In some assertive parametric circumstances, the discrete-time model has eight equilibrium points among which one is a special or unique positive equilibrium point. We have also investigated the local and global behavior of equilibrium points of an achievable three-dimensional discrete-time two predators and one prey Lotka–Volterra model. The conversion of a continuous-type model into its discrete counterpart model has been completed by adopting a dynamically consistent nonstandard difference scheme with the end goal that the equilibrium points are conserved in twin cases. The difficulty lies in how to find all fixed points O , P , Q , R , S , T , U , V and the Jacobian matrix and its characteristic polynomial at the unique positive fixed point. For that purpose, we use Mathematica software to find the equilibrium points and all of the Jacobian matrices at those equilibrium points. Moreover, we discuss boundedness conditions for every solution and prove the existence of a unique positive equilibrium point. We discuss the local stability of the obtained system about all of its equilibrium points. The discrete Lotka–Volterra model in three dimensions is given by system (3), where parameters α , β , γ , δ , ζ , η , μ , ε , υ , ρ , σ , ω ∈ R + and initial conditions x 0 , y 0 , z 0 are positive real numbers. Additionally, the rate of convergence of a solution that converges to a unique positive equilibrium point is discussed. To represent theoretical perceptions, some numerical debates are introduced, including phase portraits. [ABSTRACT FROM AUTHOR]

The effect of multiplicative stochastic perturbations on planar Hamiltonian systems is investigated. It is assumed that perturbations fade with time and preserve a stable equilibrium of the limiting system. The paper investigates bifurcations associated with changes in the stability of the equilibrium and with the appearance of new stochastically stable states in the perturbed system. It is shown that depending on the structure and the parameters of the decaying perturbations, the equilibrium can remain stable or become unstable. In some intermediate cases, a practical stability of the equilibrium with estimates for the length of the stability interval is justified. The performed stability analysis is based on a combination of the averaging method and the construction of stochastic Lyapunov functions. [ABSTRACT FROM AUTHOR]

In this paper, the potential differential game concept introduced by Fonseca-Morales and Hernández-Lerma (2018) is used in analyzing stabilization problems for n-player noncooperative capital accumulation games (CAGs). By first identifying a CAG as a potential game, an associated optimal control problem (OCP) of the CAG is obtained, whose optimal solution is an open-loop Nash equilibrium for the CAG. Compared with a saddle-point stability condition obtained for undiscounted CAG in the literature, a sufficient and easily verifiable condition is obtained for both discounted and undiscounted CAGs. In addition, the concept allows the turnpike property obtained for OCPs in Trélat and Zuazua (2015) to be verified for CAGs. Lastly, an illustrative example is given to verify the latter stability result for some CAGs. [ABSTRACT FROM AUTHOR]

Based on the underground project attached to the station of Suzhou Rail Transit Line 5, the stability of driving face of the rectangular pipe jacking was investigated. The silo and wedge model was modified, and the effective support pressure was derived based on the limit equilibrium theory. The maximum support pressure was obtained by optimization method, and the parameter analysis was carried out. The results show that the support pressure is decreased with the increasing of soil strength parameter, and it is increased with the increasing of tunnel geometry parameter. The support pressure result obtained by the optimized wedge model is greater than that by the traditional silo model, which is conducive to avoiding construction risks. The actual support pressure ( 71.00 — 90. 00 kPa) is greater than the theoretical calculation result of 51. 36 kPa, which indicates that the support pressure is suitable. The surface collapse or large settlement is presumed to be construction failure or insufficient support force due to unfavorable stratum conditions. [ABSTRACT FROM AUTHOR]

We introduce a Caputo type fractional waterborne infectious disease model. Disease transmissions of this model has saturation effect of infectious individuals on both human-to-human and environment-to-human contacts. For this model we find sufficient conditions for local stability of disease free and endemic epidemic equilibriums by linearization and global stability of disease free equilibrium by Liapunov method. Appropriate numerical simulations are also given to verify the results. [ABSTRACT FROM AUTHOR]

In this work, we revisit the planar restricted four-body problem to study the dynamics of an infinitesimal mass under the gravitational force produced by three heavy bodies with unequal masses, forming an equilateral triangle configuration. We unify known results about the existence and linear stability of the equilibrium points of this problem which have been obtained earlier, either as relative equilibria or a central configuration of the planar restricted (3 + 1) -body problem. It is the first attempt in this direction. A systematic numerical investigation is performed to obtain the resonance curves in the mass space. We use these curves to answer the question about the existing boundary between the domains of linear stability and instability. The characterization of the total number of stable points found inside the stability domain is discussed. [ABSTRACT FROM AUTHOR]

In this paper, the critical equilibrium of a simply supported compressed column on a Winkler foundation is analyzed based on Koiter's theory. The exact expression of the potential energy functional is presented. By the Fourier series of the disturbance deflection, the second-order variation of the potential energy is expressed as a quadratic form. At critical equilibrium, the second-order variation of the potential energy is semi-positive definite, so that the stability of the critical equilibrium is determined by the sign of the fourth-order variation or sixth-order variation. It can be seen that only in two small ranges of elastic-foundation stiffness is the corresponding critical state stable and the bifurcation equilibrium upward. Then, the theoretical results of this paper are compared with previous experimental and theoretical results. [ABSTRACT FROM AUTHOR]

The present study investigates the combined effects of the oblateness and straight segment on the positions and linear stability of the equilibrium points in the restricted 2 + 2 body problem. The present model holds fourteen equilibrium points, out of which six are collinear with the centers of the primaries and the rest are non-collinear. It has been observed that the positions of all the equilibrium points are subsequently affected by the oblateness and length of the primary bodies. The linear stability of the equilibrium points is also presented by slightly perturbing the position of the equilibrium points. It is observed that for a considered set of parameters, all the fourteen equilibrium points are unstable. An application of the present model is also studied, for which the position and stability of the equilibrium points are investigated for the Earth-22 Kalliope-dual satellite system. It has been observed that for this system, all the equilibrium points are unstable except for two non-collinear equilibrium points that are found to be stable. [ABSTRACT FROM AUTHOR]

In this work, the quantized Hill problem is considered in order for us to study the existence and stability of equilibrium points. In particular, we have studied three different cases which give all whole possible locations in which two points are emerging from the first case and four points from the second case, while the third case does not provide a realistic locations. Hence, we have obtained four new equilibrium points related to the quantum perturbations. Furthermore, the allowed and forbidden regions of motion of the first case are investigated numerically. We demonstrate that the obtained result in the first case is a generalization to the classical one and it can be reduced to the classical result in the absence of quantum perturbation, while the four new points will disappear. The regions of allowed motions decrease as the value of the Jacobian constant increases, and these regions will form three separate areas. Thus, the infinitesimal body can never move from one allowed region to another, and it will be trapped inside one of the possible regions of motion with the relative large values of the Jacobian constant. [ABSTRACT FROM AUTHOR]

We investigate the n-body problem on a sphere with a general interaction potential that depends on the mutual distances. We focus on the equilibrium configurations, especially on the Dziobek equilibrium configurations, which is an analogy of Dziobek central configurations of the classical n-body problem. We obtain a criterion and then reduce it to two sets of equations. Then we apply these equations to the curved n-body problem in S 3 . In the end, we find the derivative of the Cayley-Menger determinant. [ABSTRACT FROM AUTHOR]

Associating the influences of viscosity and oblateness in the finite straight segment model of the Robe's problem, the linear stability of the collinear and non-collinear equilibrium points for a small solid sphere are analyzed. This small solid sphere is moving inside the first primary which is a homogeneous incompressible viscous fluid whose hydrostatic equilibrium figure is an oblate spheroid. The second primary is a finite straight segment. The existence of the equilibrium points is discussed after deriving the pertinent equations of motion of the small solid sphere. It is found that viscosity does not affect the location and number of equilibrium points but affects the stability as it converts the marginal stability to asymptotic stability. However, oblateness affects the locations of the equilibrium points. Applicability of the results of this study to an astrophysical problem is discussed, and we have calculated a lower bound on the ratio of the orbital radius and the total mass of the primaries of an astrophysical problem to which the results obtained may be applied. This ratio is called the scaling factor. [ABSTRACT FROM AUTHOR]

In this paper, we consider the boundary-value problem for the Kuramoto–Sivashinsky equation with homogeneous Neumann conditions. The problem on the existence and stability of second-kind equilibrium states was studied in two ways: by the Galerkin method and by methods of the modern theory of infinite-dimensional dynamical systems. Some differences in results obtained are indicated. [ABSTRACT FROM AUTHOR]