Mathematical Modeling of Impact of Pollutants on Industries Based on Resource Biomass

Depletion of resources such as forestry, minerals etc. and resource-based industries such as wood and paper etc., due to rising pollution, is one of the biggest challenges which the humankind is facing today. In this paper, a mathematical model has been designed to give an insight into the effect of pollutants on natural resources which in turn affects the growth and stability of industries dependent on such biomass. The model is analyzed using stability theory of differential equations. Five dependent variables are considered in the model and some important assumptions are made. Two equilibria are found in the equilibrium analysis and conditions of local and global stability of interior equilibrium are obtained. Numerical simulation is also done to demonstrate the analytical findings. It is found in the study that as we impose an environmental tax on the polluters, the concentration of pollutants in the environment is controlled and the stable equilibrium shifts in such a way that the densities of resource biomass and dependent industries are close to the densities which correspond to the pollution free ecosystem.

Modelling of sawtooth-induced fast ion transport in positive and negative triangularity in TCV

Internal kinks are a common magneto hydro-dynamic (MHD) instability observed in tokamak operation when the q profile in the plasma core is close to unity. This MHD instability impacts both the transport of the bulk plasma (current, particle and energy transport) and minority species, such as fast ions. In TCV (R 0 /a = 0.88 m/0.25 m) the fast ion population is generated in the plasma by neutral beam tangential injection of energies up to 28 keV. TCV features 16 active shaping coils permitting a great flexibility in plasma shape, including negative triangularity (δ) configurations that show surprisingly high confinement. This study focuses on the transport of fast ions induced by sawteeth, by comparing two triangularity cases and simulation results with experimental data. Comparison of two equilibria with opposite δ shows that the fast ion drifts are larger for δ < 0. Furthermore, the sawtooth-induced transport in this case is larger than δ > 0 in similar conditions. Comparison with experimental data confirms the dominance of the modification of thermal kinetic profiles following the sawtooth crash in explaining drops in the neutron rates and FIDA signals. Additional fast ion diffusion, however, improves the interpretation of the experimental data. For δ < 0, the amplitude of the perturbation better representing the experimental data is larger. Finaly, an exploratory study for 50 keV particles (soon available in TCV) shows that the situation does not worsen for such particles.

Optimal Control of a Cell-to-Cell Fractional-Order Model with Periodic Immune Response for HCV

In this paper, a Caputo fractional-order HCV Periodic immune response model with saturation incidence, cell-to-cell and drug control was proposed. We derive two different basic reproductive numbers and their relation with infection-free equilibrium and the immune-exhausted equilibrium. Moreover, there exists some symmetry in the relationship between the two equilibria and the basic reproduction numbers. We obtain the global stability of the infection-free equilibrium by using Lyapunov function and the local stability of the immune-exhausted equilibrium. The optimal control problem is also considered and two control strategies are given; one is for ITX5061 monotherapy, the other is for ITX5061 and DAAs combination therapy. Matlab numerical simulation shows that combination therapy has lower objective function value; therefore, it is worth trying to use combination therapy to treat HCV infection.

Market Choices Driven by Reference Groups: A Comparison of Analytical and Simulation Results on Random Networks

The present paper reports simulation results for a simple model of reference group influence on market choices, e.g., brand selection. The model was simulated on three types of random graphs, Erdos–Renyi, Barabasi–Albert, and Watts–Strogatz. The estimates of equilibria based on the simulation results were compared to the equilibria of the theoretical model. It was verified that the simulations exhibited the same qualitative behavior as the theoretical model, and for graphs with high connectivity and low clustering, the quantitative predictions offered a viable approximation. These results allowed extending the results from the simple theoretical model to networks. Thus, by increasing the positive response towards the reference group, the third party may create a bistable situation with two equilibria at which respective brands dominate the market. This task is easier for large reference groups.

What to Expect from the Lower Bound on Interest Rates: Evidence from Derivatives Prices

This paper analyzes the effects of the lower bound for interest rates on the distributions of inflation and interest rates. In a New Keynesian model with a lower bound, two equilibria emerge: policy is mostly unconstrained in the “target equilibrium,” whereas policy is mostly constrained in the “liquidity trap equilibrium.” Using options data on interest rates and inflation, we find forecast densities consistent with the target equilibrium and find no evidence in favor of the liquidity trap equilibrium. The lower bound has a sizable effect on the distribution of interest rates, but its impact on inflation is relatively modest. (JEL E12, E23, E31, E43, E52, G13)

Game Theory, Tourism and Land Ethics

This paper combines game theory with Land Ethics to demonstrate a path forward for sustainable development. Our findings indicate that two likely equilibria can be reached. One equilibrium focuses on high short-term profits, but with ecological damage leading to less cumulative profits. The second equilibrium requires ecological maintenance costs (thus less short-term profits) yet yields greater cumulative profits. The comparison of the two equilibria and using the historical perspective of the Wisconsin Dells demonstrates how communities that embrace a Land Ethic can reach the equilibrium that produces greater long-term benefits.

Innovation, on-the-job learning, and labor contracts: an organizational equilibria approach

An established tenet of the literature is that the use of flexible labor leads to less innovation. Yet, less attention has been paid to the possibility that it is the decision to innovate that generates the incentive to hire on a permanent basis. The goal of this paper is to show the existence of interlocking complementarities between the firm's technological and hiring strategies. To do so, we develop a simple model where the workers’ decision to invest in human capital is affected by the type of employment contract (temporary versus permanent) and by the type of technological investments (routine versus innovative). When the firm is unable to coordinate its actions across these different domains, two equilibria simultaneously exist: in the ‘high-road’ equilibrium, firms invest more in innovative projects and hire on a permanent basis; in the ‘low-road’ equilibrium, they invest more in routine projects and hire on a temporary basis.

Analisis kestabilan dan kontrol optimal model matematika penyebaran penyakit Ebola dengan variabel kontrol berupa karantina

Ebola disease is an infectious disease caused by a virus from the genus Ebolavirus and the family Filoviridae. Ebola disease is one of the most deadly diseases for human. The purpose of the thesis is to analyze the stability of the equilibrium point and to apply the optimal control of quarantine on a mathematical model of the spread of ebola. Model without control has two equilibria, non-endemic equilibrium and endemic equilibrium. The existence of endemic equilibrium and local stability depends on the basic reproduction number (R0). The non-endemic equilibrium is asymptotically stable if R0 1 and endemic equilibrium tend to asymptotically stable if R0 1. The problem of optimal control is solved by Pontryagin’s Maximum Principle. From the numerical simulation, the result shows that control is effective enough to minimize the number of infected human population and to minimize the cost of its control.

Bifurcations in a Predator–Prey Model of Leslie-Type with Simplified Holling Type IV Functional Response

In this paper, we complete the remaining investigation of local bifurcations in a predator–prey model of Leslie-type with simplified Holling type IV functional response. The system has at most three equilibria, and local bifurcations were completely investigated in the cases of one and three equilibria, but in the case of two equilibria the previous study was only on a fixed parameter. We extend the study in the case of two equilibria for all parameters, and find that the system exhibits Hopf bifurcations of codimensions 1 and 2, and Bogdanov–Takens bifurcations of codimensions 2 and 3. Previous results and our research show that the codimension of local bifurcations is at most 3, and both focus type and cusp type Bogdanov–Takens bifurcations of codimension 3 can occur.

Dynamical analysis, circuit implementation and synchronization of a new memristive hyperchaotic system with coexisting attractors

This paper constructs a novel memristive hyperchaotic system by introducing the flux-controlled memristor to an extended jerk system. The memristive system has two equilibria and coexists two symmetric hyperchaotic attractors. The dynamic behaviors of the system are studied through bifurcation analysis. The analog circuit design and microcontroller-based experimental implementation of the system are presented. The synchronization of the system is realized by using the adaptive control technique. The sufficient conditions for synchronization are established via theoretical and numerical analysis.