Equilibrium Point Analysis Research Articles

Bifurcations of a Leslie-Gower predator-prey model with fear, strong Allee effect and hunting cooperation

<p>Considering the impact of fear levels, Allee effects and hunting cooperation factors on system stability, a Leslie-Gower predator-prey model was formulated. The existence, stability and bifurcation analysis of equilibrium points were studied by use of topological equivalence, characteristic equations, Sotomayor's theorem, and bifurcation theory. The sufficient conditions of saddle-node, Hopf, and Bogdanov-Takens bifurcations were established, respectively. Numerically, the theoretical findings were validated and some complicated dynamical behaviors as periodic fluctuation and multi-stability were revealed. The parameter critical values of saddle-node, Hopf bifurcation, and Bogdanov-Takens bifurcations were established. Biologically, how these factors of fear, Allee effect, and hunting cooperation affect the existence of equilibria and jointly affect the system dynamics were analyzed.</p>

Superconductivity coupling of harmonic resonant oscillators: Homogeneous and heterogeneous extreme multistability with multi-scrolls.

Understanding and characterizing multistabilities, whether homogeneous or heterogeneous, is crucial in various fields as it helps to unveil complex system behaviors and provides insights into the resilience and adaptability of these systems when faced with perturbations or changes. Homogeneous and heterogeneous multistabilities refer, respectively, to situation in which various multiple stable states within a system are qualitatively similar or distinct. Generating such complex phenomena with multi-scrolls from inherent circuits is less reported. This paper aims to investigate extreme multistability dynamics with homogeneous and heterogeneous multi-scrolls in two coupled resonant oscillators through a shunted Josephson junction. Analysis of equilibrium points revealed that the system supports both hidden and self-excited attractors. Various dynamical tools, including bifurcation diagrams, spectrum of Lyapunov exponents, and phase portraits, are exploited to establish the connection between the system parameters and various complicated dynamical features of the system. By tuning both system parameters and initial conditions, some striking phenomena, such as homogeneous and heterogeneous extreme multistability, along with the emergence of multi-scrolls, are illustrated. Furthermore, it is observed that one can readily control the number of scrolls purely by varying the initial conditions of the investigated system. A multi-metastable phenomenon is also captured in the system and confirmed using the finite-time Lyapunov exponents. Finally, the microcontroller implementation of the system demonstrates strong alignment with the numerical investigations.

ANALYSIS OF THE COVID-19 EPIDEMIC MODEL WITH SELF-ISOLATION AND HOSPITAL ISOLATION

This research developed the SIR model with self-isolation and hospital isolation. The analysis is carried out through the disease-free and endemic equilibrium point analysis and the sensitivity analysis of the basic reproduction number. Based on the disease-free equilibrium point analysis, for a certain period of time the population will be free from COVID-19 if the basic reproduction number is less than 1. If the basic reproduction number is more than 1, the disease will persist in the population, this will lead to an endemic equilibrium point. Based on the sensitivity analysis of parameter values on the basic reproduction number, the parameter for the isolation rate of individually infected individuals in hospitals is -0.4615166040, and the self-isolation rate at home is -0.01853667767. This indicates that isolation in hospitals is more effective than self-isolation in suppressing the spread of COVID-19.

MATHEMATICAL MODELS OF DENGUE TRANSMISSION DYNAMICS WITH VACCINATION AND WOLBACHIA PARAMETERS AND SEASONAL ASPECTS

The Aedes aegypti mosquito is the main carrier of dengue virus transmission to humans. In this study, a mathematical model for the transmission of the dengue virus is constructed using vaccination and Wolbachia parameters in an attempt to control the virus's spread. Furthermore, the fundamental reproduction number is set as a parameter of the infection threshold. Based on the stability of the equilibrium point analysis, it is found that the disease-free equilibrium point is locally asymptotically stable if . Then, a mathematical model of dengue was created by examining the seasonal aspect and adding a periodic term to the mosquito birth rate. Dengue virus transmission in mosquito populations is controlled by air temperature in addition to seasonal variables. In this study, three weather scenarios were simulated: scenario 1 for cold weather (air temperature 14 °C), scenario 2 for hot weather (air temperature 26 °C), and scenario 3 for moderate weather (air temperature between 14 and 26 °C).

GLOBAL STABILITY OF DISEASE-FREE EQUILIBRIA IN COVID-19 SPREAD THROUGH LIVING AND INANIMATE OBJECTS MATHEMATICAL MODEL

Covid-19 is a dangerous disease that is easily transmitted, both through living media in the form of interactions with infected human, as well as through inanimate objects in the form of surfaces contaminated with the Coronavirus. Various preventive and repressive efforts have been made to prevent the spread of this disease, such as isolating and recovering the infected human. In this study, the authors construct and analyze a new mathematical model in the form of a three-dimensional differential equations system that represent the interactions between subpopulations of coronavirus living on inanimate objects, susceptible human, and infected human within a population. The purpose of this study is to investigate the criteria that must be met in order to create a population free from Covid-19 by considering inanimate objects as a medium for its spread besides living objects. The model solution that represents the number of each subpopulation is non-negative and bounded, so it is in accordance with the biological condition that the number of subpopulations cannot be negative and there is always a limit for its value. The eradication rate of Coronavirus living on inanimate objects, the recovery rate of infected human, and the interaction rate between susceptible human and infected human such that the population is free from Covid-19 for any initial conditions of each subpopulation were investigated in this study through global stability analysis of the disease-free equilibrium point of the model.

Within-host mathematical model of malaria parasite with cell-mediated and antibody-mediated immune systems

ABSTRACT Malaria is a serious health problem in the world. Nearly half of the world’s population is at risk of disease. In this study, a mathematical model was developed to understand and analyze the dynamics of the malaria parasite within host cells with cell-mediated and antibody-mediated immune systems. The model categorizes the population into six compartments. The study provides a concise representation of the interaction between the parasite and red blood cells, as well as the responses of the immune system, including both antibody-mediated and cell-mediated responses. The research examines the biological visibility and well-posedness of the model, ensuring that the solutions remain bounded and positive. The basic reproduction number, which indicates the potential spread of the parasite is determined. The stability analysis of the parasite-free equilibrium point was also conducted, revealing that the parasite-free state is locally and globally stable if the basic reproduction number, R 0 < 1 . Furthermore, bifurcation and sensitivity analysis are performed. Finally, to complement the theoretical findings and illustrate the impact of immunological effectiveness, numerical simulations are conducted under different scenarios. The result shows that the cell-mediated and antibody-mediated immune response helps to eliminate the parasite within the human host.

Dynamical analysis of a novel discrete fractional lumpy skin disease model

Lumpy skin disease is a viral disease that affects cattle and is caused by the lumpy skin disease virus. This work is devoted to presenting and analyzing the nonlinear dynamics of a novel discrete fractional model for lumpy skin disease. The equilibrium points of the proposed discrete fractional model are found. The stability analysis of equilibrium points is carried out. The influences of key parameters in the model are investigated, and then the stability regions of a disease-free steady state in the space of parameters are obtained. A proposed efficient control scheme is implemented to stabilize the disease-free equilibrium point when it is unstable. The influences of fractional-order parameters on the applied control scheme are explored. Finally, numerical simulations are performed to verify the theoretical findings obtained and confirm the effectiveness of the employed control scheme.

The Dynamics of Tuberculosis through BSEIR Model with Immigration in Malaysia

Tuberculosis or known as TB is an airborne disease that exists in Malaysia caused by Mycobacterium Tuberculosis. Despite that, TB infection is curable with early diagnosis and treatment. The disease can be prevented through Bacillus Calmette-Guérin (BCG) vaccine, which is given among infants at birth. Numerous mathematical models on infectious diseases have been formulated in earlier studies since it is crucial to comprehend infectious disease transmission patterns and predict future outcomes. However, there is minimal study on the dynamics of TB transmission, particularly in Malaysia concerning immigration. Hence, this study aims to formulate a mathematical BCG-vaccinated, susceptible, exposed, infected, and recovered (BSEIR) model for TB infection in Malaysia by considering the immigration parameter. The model parameters are obtained from the literature and some with reported data in 2013 as initial value for the simulation using MAPLE software. The obtained results revealed that the basic reproduction number, for the model is more than one. The graphical plot shows that the BSEIR model with immigration demonstrates a rise in TB-infected cases. The best strategy to lessen the number of infected individuals in Malaysia is by increasing the transmission rate and recovery rate. Additionally, the local stability analysis on the diseases-free equilibrium point and sensitivity analysis of its parameter is also provided and discussed. To conclude, a proper screening test should be mandated by the authorities before permitting new immigrants and refugees into Malaysia.

Discretization and Stability Analysis for a Generalized Type Nonlinear Pharmacokinetic Models

Estimating the effects of drugs at different stages is directly proportional to the duration of recovery and the duration of pulling through with the disease. It is very important to estimate the effects of drugs at different stages. For this reason, solving Pharmacokinetic models which investigate these effects are very important. In this study, numerical solutions of one, two, and three-compartment nonlinear Pharmacokinetic models have been studied. Distributed order differential equations have been used for the solution. Numerical solutions have been found with the density function contained in distributed order differential equations and different values of this function. A nonstandard finite difference scheme has been used for numerical solutions. Finally, stability analyses of equilibrium points of the obtained discretized system have also been researched with the help of the Matignon criterion.

A new fractional-order 5D memristive chaotic system with special extreme multistability and its application to image encryption

Introducing memristor into the chaotic system can enrich the dynamic behaviors of the chaotic system. We propose a symbolic function memristor model and introduce it into a chaotic system to construct a fractional-order 5D memristor chaotic system. Through dynamic analysis of equilibrium point, Lyapunov exponents, phase diagram and bifurcation diagram, it is found that the system has abundant dynamic behaviors, for example, the change of equilibrium point type with parameters, transient chaos, offset-boosting and a special kind of extreme multistability. And with the change of parameters, the attractor state and shape will appear rich changes. Then the correctness of the system is verified by circuit simulation. The chaotic system is introduced into the process of image encryption, and an encryption system is constructed, which is composed of Zigzag scrambling, Hilbert curve scrambling, DNA encryption and GF257 diffusion algorithm. Finally, through a variety of security verification, the results show that the encryption system has good security and can resist many kinds of attacks effectively.

Promoting the Low-Carbon Transition of Power Construction Projects under MRV: An Evolutionary Game Analysis

The actual situation of carbon-emission reduction in China’s power sector has not yet achieved the expected benefits. The rent-seeking behavior of participants in power construction projects (PCPs) hinders the realization of low-carbon benefits. It is necessary to explore the behavioral strategies of the various participants in the low-carbon transition of PCPs. This paper creatively constructs an evolutionary game model of PCPs’ participants from the perspective of MRV (monitoring, reporting, and verification) and introduces the influence of the public to provide a comprehensive analysis of strategic equilibrium points. Through numerical simulations with MATLAB R2021a software, this paper explores the strategic choices of participants in different situations and gives relevant inferences and proofs. The results show that the grid company dominates at the initial stage and promotes participants to regulate behaviors. Under the premise of satisfying the system-stability requirements, setting the growth rate of the grid company’s punishments to 100% can enhance the willingness for strict supervision, while the growth rate of the supervision costs to 200% significantly decreases the probability of strict supervision. With the integration of MRV and PCPs, participants spontaneously fulfill the carbon-emission-reduction tasks. Reasonable control of input costs can effectively avoid the occurrence of rent-seeking behavior. In addition, this paper sets the public-influence growth rate at 200% and finds that the public plays a greater role in driving participants to fulfill responsibilities. Based on the results, a low-carbon transition mechanism for PCPs under the MRV system is proposed by considering several dimensions, which provides suggestions for participants to fulfill carbon-reduction responsibilities.

Dynamic Analysis of the Susceptible-Exposed-Infected-Hospitalized-Critical-Recovered-Dead (SEIHCRD)

This study discusses the dynamic analysis of the Susceptible–Exposed–Infected–Hospitalized–Critical–Recovered–Dead (SEIHCRD) model using the fourth order Runge-Kutta method. The data used in this study is original data on Infected, Hospitalized and Critical cases in Indonesia from August to October 2021. Dynamic analysis of the model is carried out by determining disease-free and endemic equilibrium points, local stability analysis of disease-free and endemic equilibrium points, and determine the basic reproduction number. The result of this analysis is that the number of new infection cases in Indonesia will decrease over time and the COVID-19 outbreak will end. Then a numerical simulation was carried out using the fourth order Runge-Kutta method in dealing with COVID-19 cases in Indonesia. The simulations and calculations show that the rate of contact of susceptible individuals with infected individuals is 0.06 per day, the rate of movement of individuals in the Exposed class to the Infected class is 0.14 per day, the probability of infected individuals being hospitalized with a value of 0.95, the probability that COVID-19 patients become critical and enter the Intensive Care Unit (ICU) with a value of 0.485, and the probability of a critical patient dying with a value of 0.25 affects the slope of Infected, Hospitalized and Critical cases in Indonesia. Where Infected cases will be sloping with an absolute error value of 28%, Hospitalized cases with an absolute error value of 20% and Critical cases with an absolute error value of 33%. This research provides information that it is estimated that the daily infection cases of COVID-19 will decrease and be close to zero. So that infected patients who must be hospitalized and admitted to the Intensive Care Unit (ICU) are also decreasing, it is hoped that the COVID-19 pandemic will not happen again

Fractional optimal control strategies for hepatitis B virus infection with cost-effectiveness analysis

Hepatitis B disease is a communicable disease that is caused by the hepatitis B virus and has become a significant health problem in the world. It is a contagious disease that is transmittable from person to person either horizontally or vertically. This current study is aimed at sensitivity analysis and optimal control strategies for a fractional hepatitis B epidemic model with a saturated incidence rate in the sense of the Caputo order fractional derivative approach. Fundamental properties of the proposed fractional order model are obtained and discussed. A detailed analysis of disease-free equilibrium and endemic equilibrium points is given by applying fractional calculus theory, which is a generalized version of classical calculus. Sensitivity indexes are calculated for the classical order model. Illustrative graphics that show the dependence of the sensitivity index on fractional order derivative for alpha in (0,1) are provided. Based on the results of the sensitivity analysis and using Pontryagin’s Maximum Principle, optimal control strategies for preventing hepatitis B infection with vaccination and treatment are considered. Fractional Euler’s method is used to carry out the numerical simulation for the proposed fractional optimal control system and the obtained results are analyzed. The results of the analysis reveal that hepatitis B disease can be prevented if necessary precautionary is taken or effective vaccination and treatment control measures are applied. The analysis of cost-effectiveness is also conducted and discussed.

Performance Analysis of Connection Establishment Procedure Under Beamforming in 5G NR Networks

High demand for reliability, low latency, seamless connectivity lead to the 5&#x00A0;G era. 5&#x00A0;G cellular networks employ a random access based preamble transmission procedure for the initial locking of User Equipment (UEs) to a base station (gNB) and uplink resource scheduling. It is of utmost importance that we evaluate the factors that aid and those that limit the random access procedure in achieving its envisaged goal. In this paper, we develop an analytical model for random access procedure for connection establishment in 5&#x00A0;G when beamforming is employed. The random access medium is modelled as a multi-channel slotted Aloha system. We use an equilibrium point analysis framework to derive the performance metrics namely, the rate at which UEs can lock on to a gNB and the average and variance of the time taken by a new UE to establish connection with the base station. We analyse the impact of the retransmission limit and the number of available preambles for random access on the performance of connection establishment of a UE. Our analysis brings out the importance of the choice of base station configurations with respect to the user demographics of a 5&#x00A0;G NR cell.

Analysis of a non-integer order mathematical model for double strains of dengue and COVID-19 co-circulation using an efficient finite-difference method

An efficient finite difference approach is adopted to analyze the solution of a novel fractional-order mathematical model to control the co-circulation of double strains of dengue and COVID-19. The model is primarily built on a non-integer Caputo fractional derivative. The famous fixed-point theorem developed by Banach is employed to ensure that the solution of the formulated model exists and is ultimately unique. The model is examined for stability around the infection-free equilibrium point analysis, and it was observed that it is stable (asymptotically) when the maximum reproduction number is strictly below unity. Furthermore, global stability analysis of the disease-present equilibrium is conducted via the direct Lyapunov method. The non-standard finite difference (NSFD) approach is adopted to solve the formulated model. Furthermore, numerical experiments on the model reveal that the trajectories of the infected compartments converge to the disease-present equilibrium when the basic reproduction number ({mathbb {R}}_0) is greater than one and disease-free equilibrium when the basic reproduction number is less than one respectively. This convergence is independent of the fractional orders and assumed initial conditions. The paper equally emphasized the outcome of altering the fractional orders, infection and recovery rates on the disease patterns. Similarly, we also remarked the importance of some key control measures to curtail the co-spread of double strains of dengue and COVID-19.

Dynamical behaviors and optimal control of delayed S2IS rumor propagation model with saturated conversion function over complex networks

Nowadays, online information is disseminated in multiple languages on different platforms, and research on the dissemination trend and control of online rumors is a topic worth discussing. In the bilingual environment, we study the S2IS rumor propagation model with time delay and saturated conversion function which implies the limitation of resources in homogeneous and heterogeneous networks. First and foremost, the analysis of the boundedness of the solutions and the existence of the rumor-spreading equilibrium points is given in our work, and we figure out the basic reproduction number. Next, we conduct the local stability analysis of the rumor-free equilibrium point and the rumor-spreading equilibrium points according to the characteristic equation. The global stability of the rumor-free equilibrium point is shown based on the Lyapunov stability theory. Besides, we study the forward and backward bifurcation phenomenon and optimal control problem in theory, which is seldom discussed in the bilingual environment. Finally, numerical simulations are performed to verify the correctness of our main results.

Analysis of Tripartite Dynamic Game Theory in Ecological Law Enforcement

The ecological governance issues of the police department have always been urgently needed to be addressed and explored. This article will take the ecological areas of the Yangtze River Basin as an example to construct a tripartite dynamic game model between police enforcement department, fishermen and fishing enterprises and the ecology of the Yangtze River Basin. Through equilibrium point analysis and MATLAB numerical simulation, the strategic evolution process of the police department and various entities is demonstrated to demonstrate the necessity of ecological law enforcement and provide relevant suggestions.

Finite-time synchronization of fractional-order chaotic system based on hidden attractors

A new 3D fractional-order chaotic system is obtained by improving the Sprott-A system and introducing the definition of fractional calculus to it. Then the new system is certified to be chaotic by studying and analyzing the phase diagram, Lyapunov exponents, and smaller alignment index tests. Then the analysis of equilibrium points finds that the new system has virtually no equilibrium points and hidden attractors. The new system is dynamically analyzed by bifurcation diagram, time-domain waveform and complexity, it is indicated that the system is susceptible to initial conditions, and with the changes of different parameters the system produced different scroll types of attractors. In addition, to verify the feasibility of the system, a simulation circuit design based on Multisim is therefore carried out. Finally, the finite-time synchronization of the fractional-order system is successfully achieved by taking advantage of the high security of the hidden attractors.

Multi-scroll Hopfield neural network under electromagnetic radiation and its brain-like coupling synchronization

Multi-scroll attractors have attracted attention because of their more complex topological structures and artificially controllable attractor structures. This paper proposes a new nonvolatile magnetic-controlled memristor and uses it to simulate the effect of membrane flux changes caused by neuronal exposure to electromagnetic radiation. A series of complex chaotic phenomena are found by plotting phase diagrams, bifurcation diagrams, attractor domains and 01 tests, including multi-scroll chaotic attractors controlled by memristors, symmetric bifurcation behavior, coexistence phenomena enhanced by initial offset. The mechanisms behind them are explained through equilibrium point analysis. A dual memristive HNN (MHNN) coupling synchronization model is proposed to simulate the synchronization between regions within the human brain. The Lyapunov function of the error is constructed to prove that this coupling synchronization scheme is ultimately bounded. The feasibility of this synchronization scheme is verified by establishing a Simulink model and conducting simulation experiments.

Transmission Analysis of Salmonella Dublin of Diary Calves

Salmonellosis is an extremely contagious disease caused by bacteria of the genus Salmonella which affects both humans and animals. Salmonella is a cause for concern in the cattle business because it is a zoonotic disease that can cause serious invasive infections in people and besides, infected herds suffer economic and welfare losses. Consequently, a SIRB (Susceptible - Infected - Recovered-Bacteria) model is being constructed to study the transmission process of the Salmonella Dublin disease in a diary calf. The associated basic reproduction number and stability theory are used to investigate the stability analysis of the model equilibrium points. Numerical simulations was carried out to investigate the effect of the sensitive parameters on the basic reproduction number R 0. Also, the impact of environmental bacteria on Salmonella transmisssion dynamics and the eradication threshold was shown to help reduce the spread of the disease.