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Transposable elements (TEs) are selfish genetic elements whose antagonistic interactions with hosts represent a common genetic conflict in eukaryotes. To resolve this conflict, hosts have widely adopted epigenetic silencing that deposits repressive marks at TEs. However, this mechanism is imperfect and fails to fully halt TE replication. Furthermore, TE epigenetic silencing can inadvertently spread repressive marks to adjacent functional sequences, a phenomenon considered a 'curse' of this conflict resolution. Here, we used forward simulations to explore how TE epigenetic silencing and its harmful side effects shape the evolutionary dynamics of TEs and their hosts. Our findings reveal that epigenetic silencing allows TEs and their hosts to stably coexist under a wide range of conditions, because the underlying molecular mechanisms give rise to copy-number dependency of the strength of TE silencing. Interestingly, contrary to intuitive expectations that TE epigenetic silencing should evolve to be as strong as possible, we found a selective benefit for modifier alleles that weaken TE silencing under biologically feasible conditions. These results reveal that the dual nature of TE epigenetic silencing, with both positive and negative effects, complicates its evolutionary trajectory and makes it challenging to determine whether TE epigenetic silencing is a 'blessing' or a 'curse'. [ABSTRACT FROM AUTHOR]

The dynamics of fish populations, even for simple classes of reproductive functions, can be quite complex (up to the manifestation of chaotic regimes). The following problem arises: how will the population behavior change when optimal long-term fishing is imposed on it? The fundamental properties of the corresponding annual catch are defined and justified. On their basis, for the first time, an unexpected result was strictly substantiated: population dynamics are greatly simplified under optimal fishing, and, in particular, chaos is transformed into a monotonic tendency of fish numbers to balance. [ABSTRACT FROM AUTHOR]

We show that the incenter of an isosceles triangle is a stable equilibrium point of the electrostatic potential of certain point charges placed at its vertices. To this end, explicit formulas for these charges are given and the hessian of their electrostatic potential is computed. The behavior of this hessian in a family of triangles with the given inscribed and circumscribed circles is investigated and its extremal values are computed. As an application, we prove that each point in the unit disc is a stable equilibrium point of a certain triple of point charges on its boundary, which yields an explicit scenario of robust electrostatic control in Euclidean discs. In conclusion, several examples are presented which show that analogous problems are interesting and feasible for convex quadrilaterals. [ABSTRACT FROM AUTHOR]

Abstract We present a deterministic SEIR model of the said form. The population in point can be considered as consisting of a local population together with a migrant subpopulation. The migrants come into the local population for a short stay. In particular, the model allows for a constant inflow of individuals into different classes and constant outflow of individuals from the R-class. The system of ordinary differential equations has positive solutions and the infected classes remain above specified threshold levels. The equilibrium points are shown to be asymptotically stable. The utility of the model is demonstrated by way of an application to measles.

Today, the use of fog computing is increasing due to the development of delay-sensitive applications in areas such as e-health, agriculture, and smart city management. In such applications, the use of partial offloading can provide better performance compared to full offloading. It means that part of the user's tasks can be offloaded to near fog devices and the rest can be performed locally for a better user experience. Unfortunately, here, users' selfishness to obtain fog device resources may lead to more complicated issues. There are various mathematical tools for modeling users' selfishness, the most common of which is game theory. Due to the NP-hard nature of the problem, the previous game-theoretical methods could not perform well when the number of users is large. Also, these methods require knowledge about other players. This paper proposes a partial offloading method based on replicator dynamics of evolutionary game theory. Here, the concept of player has been replaced by the strategy to increase scalability. Unlike previous research in which the complexity of the problem depends on the number of users, here, the number of strategies is a major concern. In addition, the proposed method does not require any hidden information from other users. It divides the population into local CPU cycles and offloaded CPU cycles, and then solves a dynamic equation to find out which of the two populations is growing. The results of solving the replicator equation followed by statistical analysis show that the proposed method has a remarkable performance improvement compared to the state-of-the-art methods. Our method, on average, results in a 17% energy saving compared to full local execution. It also reduces latency by 18% and 29% compared to full local and full offloading methods, respectively. Since the proposed method does not require hidden information about users, it can reduce the overhead by 15% compared to the local execution method. [ABSTRACT FROM AUTHOR]

Cloud service has great convenience, because of its complex structure and dynamic nature, it is difficult to choose the best cost-effective strategy in the process of security and privacy information. To solve this problem, we construct a quantitative benefit of game strategy, use evolutionary game theory to build a game model of attack protection, propose the optimal protection strategy selection algorithm, and make the stable equilibrium solution based on limited rational constraints. Because of the inter dependency among the strategies in the same game group, we use the incentive coefficient to improve the classical dynamic replication equation, establish an improved attack protection evolutionary game model, further discuss and analyze the stability of the equilibrium point based on Jacobian matrix method, and give the optimal selection strategy under different conditions. Finally, we show the correctness, credibility, and effectiveness of the model through experiments; different strategies of the same group have the dual effects of promotion and inhibition, and show the characteristics and advantages of this paper by comparing with other literatures. [ABSTRACT FROM AUTHOR]

We present a deterministic SEIR model of the said form. The population in point can be considered as consisting of a local population together with a migrant subpopulation. The migrants come into the local population for a short stay. In particular, the model allows for a constant inflow of individuals into different classes and constant outflow of individuals from the R-class. The system of ordinary differential equations has positive solutions and the infected classes remain above specified threshold levels. The equilibrium points are shown to be asymptotically stable. The utility of the model is demonstrated by way of an application to measles. [ABSTRACT FROM AUTHOR]

This paper gives some new insights into a chaotic system. The considered system has only one Lyapunov stable equilibrium and positive Lyapunov exponent in some certain parameter range, which means there coexists chaotic attractors and Lyapunov stable equibirium in system. First, from the perspective of analyzing the global structure of the system, based on the Poincaré compactification technique, the complete description of its dynamical behavior on the sphere at infinity is presented. The obtaining results show that its global dynamical behavior is very complex. Second, from a geometric perspective, the Jacobi stability of the system is investigated, including the unique equilibrium and a periodic orbit. Interestingly, we find that the unique Lyapunov stable equilibrium is always Jacobi unstable, a Lyapunov stable periodic orbit falls into both Jacobi stable and Jacobi unstable regions. It is shown that we might witness chaotic behavior of the system before the trajectories enter a neighborhood of the equilibrium point. It is hoped that the investigation of this paper can contribute to better understand and study the complex chaotic system with stable equilibria. [ABSTRACT FROM AUTHOR]

This paper proposes a new three-dimensional chaotic flow with one stable equilibrium. Dynamical properties of this system are investigated. The system has a chaotic attractor coexisting with a stable equilibrium. Thus the chaotic attractor is hidden. Basin of attractions shows the tangle of different attractors. Also, some complexity measures of the system such as Lyapunov exponent and entropy will are analyzed. We show that the Kolmogorov-Sinai Entropy shows more accurate results in comparison with Shanon Entropy.

This paper reports a simple three-dimensional autonomous system with a single stable node equilibrium. The system has a constant controller which adjusts the dynamic of the system. It is revealed that the system exhibits both chaotic and non-chaotic dynamics. Moreover, chaotic or periodic attractors coexist with a single stable equilibrium for some control parameter based on initial conditions. The system dynamics are studied by analyzing bifurcation diagrams, Lyapunov exponents, and basins of attractions. Beyond a fixed-point analysis, a new analysis known as connecting curves is provided. These curves are one-dimensional sets of the points that are more informative than fixed points. These curves are the skeleton of the system, which shows the direction of flow evolution.

This article introduces a new simple jerk system with sine hyperbolic nonlinearity which gives the hidden attractor. An autonomous simple implementation of jerk system experiences an important and striking feature of hidden attractors with both stable equilibrium and unstable equilibrium using a reverse nonlinearity function with parametrically controlled approach. Some basic properties of the system are well studied and analyzed in terms of route to chaos, basins of attraction, Lyapunov exponent (LE), bifurcation sequences, coexistence of attractor and phase portraits. The chaotic behavior of the new system is investigated through numerical simulation and their equivalent electrical circuit implementation using single amplifier with few passive elements. The justification of theoretical observation of the proposed chaotic system is perfectly observed in PSPICE simulation and laboratory experiment. [ABSTRACT FROM AUTHOR]

Recent evidences suggest that complex behavior such as chaos can be observed in a nonlinear system with stable equilibria. However, few studies have investigated chaotic systems with only one stable equilibrium. This paper introduces a new 3-D chaotic system having only one stable equilibrium. Dynamics of the new system are discovered by using phase portraits, basin of attraction, bifurcation diagram, and maximal Lyapunov exponents. It is interesting that the system has a state variable related with the freedom of offset boosting. In addition, we have investigated the anti-synchronization of the system via an adaptive control. Furthermore, the feasibility of the system is also discussed through presenting its electronic circuit implementation.

This paper shows some examples of chaotic systems for the six types of only one hyperbolic equilibrium in changed chameleon-like chaotic system. Two of the six cases have hidden attractors. By adjusting the parameters in the system and controlling the stability of only one equilibrium, we can further obtain chaos with four kinds of conditions: (1) index-0 node; (2) index-3 node; (3) index-0 node foci; (4) index-3 node foci. Based on the method of focus quantities, we study three limit cycles (the outmost and inner cycles are stable, and the intermediate cycle is unstable) bifurcating from an isolated Hopf equilibrium. In addition, one periodic solution can be obtained from a nonisolated zero-Hopf equilibrium. The system may help us in better understanding, revealing an intrinsic relationship of the global dynamical behaviors with the stability of equilibrium point, especially hidden chaotic attractors. [ABSTRACT FROM AUTHOR]

The literature reports the proofs that entropy is an inherent property of any system in any state and governs thermal energy, which depends on temperature and is transferred by heat interactions. A first novelty proposed in the present study is that mechanical energy, determined by pressure and transferred by work interactions, is also characterized by the entropy property. The second novelty is that a generalized definition of entropy relating to temperature, chemical potential and pressure of many-particle systems, is established to calculate the thermal, chemical and mechanical entropy contribution due to heat, mass and work interactions. The expression of generalized entropy is derived from generalized exergy, which in turn depends on temperature, chemical potential and pressure of the system, and by the entropy-exergy relationship constituting the basis of the method adopted to analyze the available energy and its transfer interactions with a reference system which may be external or constitute a subsystem. This method is underpinned by the Second Law statement enunciated in terms of existence and uniqueness of stable equilibrium for each value of energy content of the system. The equality of chemical potential and equality of pressure are assumed, in addition to equality of temperature, to be necessary conditions for stable equilibrium.

Recently developed toy models for the mean-field games of corruption and botnet defence in cyber-security with three or four states of agents are extended to a more general mean-field-game model with 2d states, d∈N. In order to tackle new technical difficulties arising from a larger state-space we introduce new asymptotic regimes, namely small discount and small interaction asymptotics. Moreover, the link between stationary and time-dependent solutions is established rigorously leading to a performance of the turnpike theory in a mean-field-game setting. [ABSTRACT FROM AUTHOR]

A physically based theory for equilibrium fluvial landscapes undergoing transport‐limited or detachment‐limited erosion is derived from equations for water flow, erosion, and hillslope stability. A scaling analysis of the equations identifies submodels for overland and channelized flows. The channel‐slope boundary (CSB) defines the interface between the two flow environments, marking the bifurcation of stable overland flows into unstable sheet flows and stable channel flows. The characteristics of CSBs are derived from an equilibrium condition of the hillslope submodel and stability conditions derived from the time‐dependent model. Equilibrium hillslopes are characterized by proportional flows of water and sediment, uniformly constant and maximum values of water flow (qc) and slope occurring on the CSB, and the minimization of a Lagrangian function of energy. Equilibrium solutions are readily derived for laminar overland flows. Power law sediment transport functions for channel flow lead to stable self‐similar solutions for channel segments characterized by realistic hydraulic geometries. Uniform equilibrium inflows qc result in straight segments of channel that are combinable into networks satisfying admissibility constraints. The aggregate length of CSB upstream of any network point determines total channel discharge and hence channel slope and elevation, providing boundary conditions that determine hillslope elevations. Large equilibrium landmasses with rainfall rate R have relatively uniform drainage densities D d = R / 2 q c. Changes to channel networks induced by environmental fluctuations may occur at any network location because maximum, neutrally stable overland flows qc occur on the CSB. Stable equilibrium surfaces are conjectured to correspond to local minima of the Lagrangian over the space of admissible networks. [ABSTRACT FROM AUTHOR]

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