Coexistence Point Research Articles

Bifurkasi Hopf pada Model Lotka-Volterra Orde-Fraksional dengan Efek Allee Aditif pada Predator

This article aims to study the dynamics of a Lotka-Volterra predator-prey model with Allee effect in predator. According to the biological condition, the Caputo fractional-order derivative is chosen as its operator. The analysis is started by identifying the existence, uniqueness, and non-negativity of the solution. Furthermore, the existence of equilibrium points and their stability is investigated. It has shown that the model has two equilibrium points namely both populations extinction point which is always a saddle point, and a conditionally stable co-existence point, both locally and globally. One of the interesting phenomena is the occurrence of Hopf bifurcation driven by the order of derivative. Finally, the numerical simulations are given to validate previous theoretical results.

Analisis Kestabilan Model Predator-Prey dengan Infeksi Penyakit pada Prey dan Pemanenan Proporsional pada Predator

The dynamics of predator-prey model with infectious disease in prey and harvesting in predator is studied. Prey is divided into two compartments i.e the susceptible prey and the infected prey. This model has five equilibrium points namely the all population extinction point, the infected prey and predator extinction point, the infected prey extinction point, and the co-existence point. We show that all population extinction point is a saddle point and therefore this condition will never be attained, while the other equilibrium points are conditionally stable. In the end, to support analytical results, the numerical simulations are given by using the fourth-order Runge-Kutta method.

A phase transition in a Curie-Weiss system with binary interactions

A single-sort continuum Curie-Weiss system of interacting particles is studied. The particles are placed in the space $\mathbb{R}^d$ divided into congruent cubic cells. For a region $V\subset \mathbb{R}^d$ consisting of $N\in \mathbb{N}$ cells, every two particles contained in $V$ attract each other with intensity $J_1/N$. The particles contained in the same cell are subjected to binary repulsion with intensity $J_2>J_1$. For fixed values of the temperature, the interaction intensities, and the chemical potential the thermodynamic phase is defined as a probability measure on the space of occupation numbers of cells, determined by a condition typical of Curie-Weiss theories. It is proved that the half-plane $J_1\,\times\,$\textit{chemical potential} contains phase coexistence points at which there exist two thermodynamic phases of the system. An equation of state for this system is obtained.

Neimark–Sacker bifurcation analysis in an intraguild predation model with general functional responses

We analyse the dynamics of a discrete system coming from an intraguild food web model by using the average method. The intraguild predation model is formed by three populations corresponding to prey (P), mesopredator (MP) and superpredator (SP), where these last two populations are specialist. We give sufficient condition to guarantee the existence of a coexistence point at which the intraguild predation discrete model undergoes a Neimark–Sacker bifurcation independently of the functional responses that govern the interactions. We show numerical applications that consist in to assume that P has logistic growth and that the relation of MP–P is through a Holling type II functional response. Besides, we will consider that the interaction of MP–P is such that population MP has defense. The interaction of SP–P will be through a Holling functional response type III or IV. In particular, we give sufficient conditions to guarantee that the three species coexist. The techniques used to obtain the results can be applied to other models with different functional responses.

Dynamics of a Fractional-Order Predator-Prey Model with Infectious Diseases in Prey

In this paper, a dynamical analysis of a fractional-order predator-prey model with infectious diseases in prey is performed. First, we prove the existence, uniqueness, non-negativity, and boundedness of the solution. We also show that the model has at most five equilibrium points, namely the origin, the infected prey and predator extinction point, the infected prey extinction point, the predator extinction point, and the co-existence point. For the first four equilibrium points, we show that the local stability properties of the fractional-order system are the same as the first-order system, but for the co-existence point, we have different local stability properties.We also present the global stability of each equilibrium points except for the origin point. We observe an interesting phenomenon, namely the occurrence of Hopf bifurcation around the co-existence equilibrium point driven by the order of fractional derivative. Moreover, we show some numerical simulations based on a predictor-corrector scheme to illustrate the result of our dynamical analysis.

Exact large deviation statistics and trajectory phase transition of a deterministic boundary driven cellular automaton.

We study the statistical properties of the long-time dynamics of the rule 54 reversible cellular automaton (CA), driven stochastically at its boundaries. This CA can be considered as a discrete-time and deterministic version of the Fredrickson-Andersen kinetically constrained model (KCM). By means of a matrix product ansatz, we compute the exact large deviation cumulant generating functions for a wide range of time-extensive observables of the dynamics, together with their associated rate functions and conditioned long-time distributions over configurations. We show that for all instances of boundary driving the CA dynamics occurs at the point of phase coexistence between competing active and inactive dynamical phases, similar to what happens in more standard KCMs. We also find the exact finite size scaling behavior of these trajectory transitions, and provide the explicit "Doob-transformed" dynamics that optimally realizes rare dynamical events.

Stability of a stage-structure Rosenzweig-MacArthur model incorporating Holling type-II functional response

The local stability of the Rosenzweig-MacArthur predator-prey system with Holling type-II functional response and stage-structure for prey is studied in this paper. It is shown that the model has three equilibrium points. The trivial equilibrium point is always unstable while two other equilibrium points, i.e., the predator extinction point and the coexistence point, are conditionally stable. When the predation process on prey increases, the number of predator increases. If the predation rate is less than or equal to the reduction rate of the predator, then the predator will go to extinct. By using the Routh-Hurwitz criterion, the local stability of the interior equilibrium point is investigated. It is also shown that the model undergoes a Hopf-bifurcation around the coexisting equilibrium point. The dynamics of the system are confirmed by some numerical simulations.

Local Stability of Coexistence Point for Trophic Interaction Dynamics

Local Stability of Coexistence Point for Trophic Interaction Dynamics

Phase Equilibria of Solid and Fluid Phases from Molecular Dynamics Simulations with Equilibrium and Nonequilibrium Free Energy Methods.

In this work, we present a methodology to determine phase coexistence lines for atomic and rigid molecular systems with an emphasis on solid-fluid and on solid-solid equilibria. Phase coexistence points are found by computing the absolute free energy for each candidate phase separately. For solid phases, a combination of the extended Einstein crystal and the Einstein molecule method is presented which constitutes a convenient way to compute the absolute free energy with fixed center of mass. We compare results from equilibrium methods-thermodynamic integration and reweighting using the multistate Bennett acceptance ratio estimator (MBAR)-with simulations using a nonequilibrium method and discuss their advantages and disadvantages. Once absolute free energies of different phases are available, they are combined with simulations performed in the isothermal isobaric ensemble and MBAR, which enables efficient, iterative tracing of coexistence lines. The method is applicable to both liquid-solid as well as solid-solid transitions and is comparably simple and convenient to apply since the same method (MBAR) is used to compute free energies and to trace the coexistence line. Furthermore, statistical uncertainties can readily be computed in a transparent manner. We apply the method to an atomic solid (fcc argon) as well as small molecular systems (methanol and water) using the LAMMPS simulation package. Our study shows that all methods can be used to reliably compute the absolute free energy of solid phases, while MBAR is the most flexible method with high statistical efficiency. We find the nonequilibrium method is an attractive choice since it is simple to set up and to postprocess and is, hence, less prone to errors. The presented workflow provides a flexible, efficient, and robust way to compute phase diagrams using openly available software.

Stability and electronic circuit implementation of Lotka–Volterra model with delay

ABSTRACT In this work, we study a Lotka–Volterra system with delay. We carry out an analytical study from which there emerge three equilibrium points. In the absence of delay, two of these points are unstable whatever the choice of the parameters of the system, and the other one is stable according to the chosen parameters. With delay, and looking only at the point of positive coexistence, we find that it can cause not only instability, oscillations and switching stabilities, but also chaos. In addition, the analytical study revealed the phenomenon of switch stability, thus increasing the zones of instability. Time traces, phase portraits and bifurcation diagram obtained by numerical simulations complement the analytical investigations. Finally, we propose an electronic circuit with delay whose simulation presents the different phenomena observed numerically, thus validating this new electronic circuit with complex dynamics.

Supercritical and subcritical Hopf-bifurcations in a two-delayed prey–predator system with density-dependent mortality of predator and strong Allee effect in prey

One of the possible ways to visualize the effect of intra- and inter-species synergistic and antagonistic interactions in a natural ecosystem is the detailed analysis of the underlying prey-predator model, and the subsequent analytical findings may provide a definite justification towards the species coexistence, which often maintains biodiversity in nature. Here, our central motivation is to understand the combined effect of the Allee threshold and intra-species competition on the evolution of interacting species, which often experience delays in evolution due to its complex ecological and physiological processes. Therefore, in the present paper, we extensively analyze the stability of a two-delayed prey-predator system in the presence of strong Allee effects in prey and intra-species competition in predator. In addition, we capture the reality of time difference between the lifespan of the prey and predator through proper nondimensionalization. The two delays in the proposed retarded system correspond to the intra-specific competition-induced feedback time lag to the prey and predator gestation period. In the absence of intra-predator competition, the present dynamics unveils supercritical Hopf-bifurcation around the interior point of coexistence which is in-line with the existing literature. It is noteworthy to mention that the proposed Allee system exhibits subcritical Hopf-bifurcation in the presence of intra-species competition in predator. We confirm the occurrence of both supercritical and subcritical Hopf-bifurcations via calculating the direction and stability of Hopf-bifurcating periodic solutions using the normal form method and the center manifold theory. Moreover, the suggested delayed schema presents supercritical Hopf-bifurcation at the boundary steady-state, where the population density of prey exists at its maximum carrying capacity. We recognize the bistability between extinction and coexistence, and the proposed model also exhibits the ‘chaotic concurrence between prey and predator,’ which happens through the period-doubling bifurcation. The existence of chaos is validated using the estimated power spectrum and the spectrum of Lyapunov exponents. The primary finding of this paper is that Allee threshold induces the capability to the density-dependent death rate of predator towards changing the stability of ‘oscillatory coexistence between prey and predator.’

Order–Disorder Phase Equilibria of Regioregular Poly(3-hexylthiophene-2,5-diyl) Solution

The cloud-point curves for solutions of regioregular poly(3-hexylthiophene-2,5-diyl) (P3HT) in o-dichlorobenzene as a function of composition were measured using a thermooptical analysis method. The binary polymer solution shows phase equilibria between a single coiled polymer in solution and polymer in nanocrystalline aggregation, in which the coexistence points at the melting temperature (i.e., solid–liquid equilibria) could be described by the theory of melting point depression combined with the Flory–Huggins model. Through the correlation of theory and experimental data, the heat of fusion per crystalline repeat unit (ΔHu = 47.5 J/g) and the binary interaction parameter (χ = 32.6/T) were estimated. When the solutions were further characterized using UV–vis spectroscopy and X-ray diffraction (XRD), the absorption spectra showed a red-shift (λmax = 464 to 518 nm) with increasing P3HT concentration from 0.01 to 6 wt %, and the XRD data displayed a trace of (100) peaks at 2θ = 5.39° with d-spacing of 1.6 ...

On Instability Pockets and Influence of Damping in Parametrically Excited Systems

In most parametrically excited systems, stability boundaries cross each other at several points to form closed unstable subregions commonly known as “instability pockets.” The first aspect of this study explores some general characteristics of these instability pockets and their structural modifications in the parametric space as damping is induced in the system. Second, the possible destabilization of undamped systems due to addition of damping in parametrically excited systems has been investigated. The study is restricted to single degree-of-freedom systems that can be modeled by Hill and quasi-periodic (QP) Hill equations. Three typical cases of Hill equation, e.g., Mathieu, Meissner, and three-frequency Hill equations, are analyzed. State transition matrices of these equations are computed symbolically/analytically over a wide range of system parameters and instability pockets are observed in the stability diagrams of Meissner, three-frequency Hill, and QP Hill equations. Locations of the intersections of stability boundaries (commonly known as coexistence points) are determined using the property that two linearly independent solutions coexist at these intersections. For Meissner equation, with a square wave coefficient, analytical expressions are constructed to compute the number and locations of the instability pockets. In the second part of the study, the symbolic/analytic forms of state transition matrices are used to compute the minimum values of damping coefficients required for instability pockets to vanish from the parametric space. The phenomenon of destabilization due to damping, previously observed in systems with two degrees-of-freedom or higher, is also demonstrated in systems with one degree-of-freedom.

Extinction dynamics from metastable coexistences in an evolutionary game.

Deterministic evolutionary game dynamics can lead to stable coexistences of different types. Stochasticity, however, drives the loss of such coexistences. This extinction is usually accompanied by population size fluctuations. We investigate the most probable extinction trajectory under such fluctuations by mapping a stochastic evolutionary model to a problem of classical mechanics using the Wentzel-Kramers-Brillouin (WKB) approximation. Our results show that more abundant types in a coexistence may be more likely to go extinct first, in good agreement with previous results. The distance between the coexistence and extinction points is not a good predictor of extinction either. Instead, the WKB method correctly predicts the type going extinct first.

Catholic politics and creating trust in eighteenth-century England

In eighteenth-century law and print, English Catholics were portrayed as entirely untrustworthy, and their exclusion from all aspects of English society encouraged. Yet, as many local studies have shown, there were numerous individual cases of relatively peaceful coexistence between Protestants and Catholics in this period. This article explores why this was the case by examining how Catholics overcame labels of untrustworthiness on a local level. Using the remarkable political influence of one high-status Catholic in the first half of the eighteenth century as a case study, it questions the utility of “pragmatism” as an explanation for instances of peaceful coexistence in this period. Instead it focuses on the role that deliberate Catholic resistance to legal disabilities played in allowing them to be considered as trustworthy individuals in their localities. The resulting picture of coexistence points towards a moderation of the historiographical emphasis on mutual compromise between confessions in favour of attention to the determined resilience of minority groups. In explaining this, this article makes the broader point that the influence of trust, long important in studies of early modern economic, political, and social relationships, is ripe for exploration in the context of interconfessional relations.

Ground-state phase diagram, fermionic entanglement and kinetically-induced frustration in a hybrid ladder with localized spins and mobile electrons

We introduce an exactly solvable hybrid spin-ladder model containing localized nodal Ising spins and interstitial mobile electrons, which are allowed to perform a quantum-mechanical hopping between the ladder’s legs. The quantum-mechanical hopping process induces an antiferromagnetic coupling between the ladder’s legs that competes with a direct exchange coupling of the nodal spins. The model is exactly mapped onto the Ising spin ladder with temperature-dependent two- and four-spin interactions, which is subsequently solved using the transfer-matrix technique. We report the ground-state phase diagram and compute the fermionic concurrence to characterize the quantum entanglement between the pair of interstitial mobile electrons. We further provide a detailed analysis of the local spin ordering including the pair and four-spin correlation functions around an elementary plaquette, as well as, the local ordering diagrams. It is shown that a complex sequence of distinct local orderings and frustrated correlations takes place when the model parameters drive the investigated system close to a zero-temperature triple coexistence point.

Phase Equilibria at Ti–Al Interface Under Low Oxygen Pressure

In this paper, thirty-nine phases in the Ti-Al-O system at high temperatures have been analyzed through thermodynamic calculations. A Ti-Al-O isothermal stability diagram was obtained from the thermochemical data. The diagrams described the equations for Ti/Al intermetallic compounds at Al2O3/TixAly and Al2O3/TiAl2O5 interfaces, and their corresponding regions. Four univariant equilibria points and ten bivariant equilibria lines at 1000 K were obtained. The equations for the coexistence points and interface lines were also obtained. A three-domain diagram of Ti-Al-O phase arrangement at temperatures between 1000 K and 1200 K was shown. Thermodynamic calculations confirmed that the formation of titanium aluminate spinel (TiAl2O5) requires a threshold TiO2 activity and a partial pressure of oxygen. In the Ti-Al-O system, when aTiO2 < 0.121 and log PO2 < –47.2 atm, TiAl2O5, TiO2, and Al2O3 compounds are not formed at 1000 K; while at the Ti/Al interfaces, compounds are formed in the order of Ti3Al(s) → TiAl(s) → TiAl2(s) → TiAl3(s).

Temporal disorder does not forbid discontinuous absorbing phase transitions in low-dimensional systems.

Recent papers have shown that spatial (quenched) disorder can suppress discontinuous absorbing phase transitions. Conversely, the scenario for temporal disorder is still unknown. To shed some light in this direction, we investigate its effect in three different two-dimensional models which are known to exhibit discontinuous absorbing phase transitions. The temporal disorder is introduced by allowing the control parameter to be time dependent p→p(t), either varying as a uniform distribution with mean p[over ¯] and variance σ or as a bimodal distribution, fluctuating between a value p and a value p_{l}≪p. In contrast to spatial disorder, our numerical results strongly suggest that such uncorrelated temporal disorder does not forbid the existence of a discontinuous absorbing phase transition. We find that all cases are characterized by behaviors similar to their pure (without disorder) counterparts, including bistability around the coexistence point and common finite-size scaling behavior with the inverse of the system volume, as recently proposed [M. M. de Oliveira et al., Phys. Rev. E 92, 062126 (2015)PLEEE81539-375510.1103/PhysRevE.92.062126]. We also observe that temporal disorder does not induce temporal Griffiths phases around discontinuous phase transitions, at least not for d=2.

The phase equilibria of multicomponent gas hydrate in methanol/ethylene glycol solution based formation water

In this paper, the three-phase coexistence points are generated for multicomponent gas hydrate in methanol (MeOH) solution for (0.05, 0.10, 0.15, and 0.35) mass fraction and ethylene glycol (EG) solution for (0.05, 0.10, 0.15, 0.35, 0.40 and 0.55) mass fraction. The phase equilibrium curves of different system were obtained by an isochoric pressure-search method on high pressure apparatus. The phase equilibrium regions of multicomponent gas hydrate were measured using the same composition of natural gas distributed in the South China Sea. And the different concentration solutions were prepared based formation water. The experimental data were measured in a wide range temperature from 267.74 to 298.53K and a wide range pressure from 4.22MPa to 34.72MPa. The results showed that the hydrate phase equilibrium curves shifted to the inhibition region in accordance with the increased inhibitor concentration. In addition, the equilibrium temperature would decrease about 2.7K when the concentration of MeOH increased 0.05 mass fraction. Besides, the suppression temperature was 1.25K with the 0.05 mass fraction increase of EG concentration in the range of 0.05 mass fraction to 0.15 mass fraction. While in high EG concentration region, the suppression temperature was 3.3K with the same increase of EG concentration (0.05 mass fraction).

Field orientation dependence of magnetization reversal in thin films with perpendicular magnetic anisotropy

The magnetization reversal process of hexagonal-close-packed (hcp) (0001) oriented Co and Co90Ru10 thin films with perpendicular magnetic anisotropy (PMA) has been studied as a function of temperature and applied magnetic field angle. Room temperature pure cobalt exhibits two characteristic reversal mechanisms. For angles near in-plane field orientation, the magnetization reversal proceeds via instability of the uniform magnetic state, whereas in the vicinity of the out-of-plane (OP) orientation, magnetization inversion takes place by means of domain nucleation. Temperature dependent measurements enable the modification of the magnetocrystalline anisotropy and reveal a gradual disappearance of the domain nucleation process during magnetization reversal for elevated temperatures. Ultimately, this suppression of the domain nucleation process leads to the exclusive occurrence of uniform state instability reversal for all field orientations at sufficiently high temperature. Comparative magnetic measurements of Co90Ru10 alloy samples allow the identification and confirmation of the high temperature remanent magnetization state of cobalt as an OP stripe domain state despite the reduction of magnetocrystalline anisotropy. Detailed micromagnetic simulations supplement the experimental results and corroborate the physical understanding of the temperature dependent behavior. Moreover, they enable a comprehensive identification of the complex energy balance in magnetic films with PMA, for which three different magnetic phases occur for sufficiently high anisotropy values, whose coexistence point is tricritical in nature.