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In this article, the local dynamics of a discrete-time Covid-19 pandemic model based on the Lotka Volterra model with topological classifications, bifurcation analysis and chaos control are investigated. It is shown that under some parametric conditions, the discrete-time Covid-19 pandemic model has two equilibrium points. With linear stability theory, local dynamics are investigated with topological classifications about the equilibrium points of the discrete-time Covid-19 epidemic model. In addition, the existence of a Neimark-Sacker bifurcation at the internal equilibrium point is proved and this bifurcation is analysed using explicit criteria. Furthermore, the chaos in the discrete Covid-19 pandemic model is also investigated with the OGY feedback control strategy. Lastly, illustrative examples are given to verify the theoretical findings. The parameter values of presented model were taken from Covid-19 data in Saudi Arabia between 18 November 2020 and 18 March 2020 for ensuring biological realism. [ABSTRACT FROM AUTHOR]

In this paper we classify the phase portraits in the Poincaré disk of the Smooth and Discontinuous (SD) Hamiltonian system with the rational Hamiltonian function H (x , y) = y 2 / 2 + P (x) / Q (x , y) , where P (x) = a , ax, a x 2 and Q (x , y) = A x 2 + B y 2 + C . [ABSTRACT FROM AUTHOR]

Discrete-time systems are sometimes used to explain natural phenomena that happen in non-linear sciences. We study the periodicity, boundedness, oscillation, stability, and certain exact solutions of nonlinear difference equations of generalized order in this paper. Using the standard iteration method, exact solutions are obtained. Some well-known theorems are used to test the stability of the equilibrium points. Some numerical examples are also provided to confirm the theoretical work's validity. The numerical component is implemented with Wolfram Mathematica. The method presented may be simply applied to other rational recursive issues. In this research, we examine the qualitative behavior of rational recursive sequences provided that the initial conditions are arbitrary real numbers. We examine the behavior of solutions on graphs according to the state of their initial value xn+1 = xnxn-8/ ±xn-7 ± xnxn-7xn-8, n ε N0. [ABSTRACT FROM AUTHOR]

This paper seeks to explore the stability assessment of a generalist predator-prey system with predator harvesting. The study presents a model examining the dynamics between primary prey and predator, considering the existence of a generalist predator. Prey growth follows a logistic rate, while predator consumption is modeled with a cyrtoid functional response. In the absence of primary prey, the predator population adopts a generalist strategy, akin to the Beverton-Holt model. The model also incorporates harvesting on the predator population. We analyze the model's equilibrium, stability, positivity, and boundedness, and use numerical simulations to explore its predictions. This study enhances our understanding of ecological interactions and supports the development of effective conservation and management strategies. [ABSTRACT FROM AUTHOR]

In this paper, a nonlinear mathematical model of COVID-19 was formulated. We proposed a SEIQR model using a system of ordinary differential equations. COVID-19 free equilibrium and endemic equilibrium points of the model are obtained. The next-generation matrix investigates a basic reproduction number of the model. The stability analysis of the model equilibrium points was investigated using basic reproduction numbers. The results show that the diseasefree equilibrium of the COVID-19 model is stable if the primary reproduction number is less than unity and unstable if the basic reproduction number is greater than unity. Sensitivity analysis was rigorously analyzed. Finally, numerical simulations are presented to illustrate the results. [ABSTRACT FROM AUTHOR]

This paper seeks to explore the stability assessment of a generalist predator-prey system with predator harvesting. The study presents a model examining the dynamics between primary prey and predator, considering the existence of a generalist predator. Prey growth follows a logistic rate, while predator consumption is modeled with a cyrtoid functional response. In the absence of primary prey, the predator population adopts a generalist strategy, akin to the Beverton-Holt model. The model also incorporates harvesting on the predator population. We analyze the model's equilibrium, stability, positivity, and boundedness, and use numerical simulations to explore its predictions. This study enhances our understanding of ecological interactions and supports the development of effective conservation and management strategies.

This paper presents a dynamic model for the transmission of schistosomiasis, which involves two definitive hostshumans and bovinesand an intermediate host, snails. The study demonstrates the positive invariance and non-negativity of the system. It outlines the conditions necessary for the existence of both disease-free and endemic equilibrium points. Additionally, it provides criteria for the local and global stability of the disease-free equilibrium point. The local stability of the endemic equilibrium point is analyzed using central manifold theory, while global stability is established through the construction of a Lyapunov function, simultaneously proving the existence of forward bifurcation in the system. A sensitivity analysis of the basic reproduction number concerning various parameters reveals that the effective contact rate between hosts and cercariae, along with the hatching rate of cercariae, are critical factors influencing the extinction of schistosomiasis. Consequently, strategies such as minimizing contact between humans and livestock in freshwater contaminated with cercariae, as well as effectively eliminating schistosomiasis eggs, can be implemented to control the disease’s spread. [ABSTRACT FROM AUTHOR]

Considering the factors such as time delay in the propagation of rumors and the inability to spread rumors due to the forced silence of network regulators, in this study, based on the SIR model, combined with the rumorrefuging mechanism and the space theory, nodes in the network were divided into susceptible node S, infective node I, rumor-refuging node C and recovered node R, a new SICR rumor propagation model was proposed. Firstly, the dynamic equation of rumor propagation in homogeneous network structure was given by means of average field theory, the existence of equilibrium point was analyzed, and the basic reproduction number of the model was calculated by using the next generation matrix method. It was found that the basic reproduction number was related to the propagation rate, average degree, migration rate, migration rate, forced silence rate, and recovery rate of infective nodes. Secondly, the local asymptotic stability of the equilibrium point was analyzed by Routh-Hurwitz criterion, and the global asymptotic stability was analyzed by LaSalle's invariance principle. Finally, the correctness of the theoretical results was verified by numerical simulation experiments. The simulation results showed that SICR model considering the rumor-refuting mechanism could suppress the rumor propagation better than SIR model. Based on Dataset_R6 dataset, the parameters of the model were fitted by least square method, and the R2 of the model was 0. 950 8. [ABSTRACT FROM AUTHOR]

The present paper explores a four-dimensional mathematical model with viral infection of plankton bloom in a phytoplankton-zooplankton, Mathematical modeling on plankton dynamics is a great interest in researchers. Here we discuss the mass action law for nutrient. We also discuss the existence and local stability of equilibrium points. To investigate the biological implication of threshold parameters and community structure. We analysis the local stability of interior equilibrium point and hopfrbifurcation. Also discuss the Permanence of the system for future time. In this paper we observed that stable distribution, periodic oscillation and periodic solution. [ABSTRACT FROM AUTHOR]

The exploration of small bodies in our solar system is of great interest for the planetary science community due to their high scientific value. However, their generally weak and irregular gravity fields increase the difficulty associated with close proximity operations. Moreover, solar radiation pressure (SRP) can significantly perturb the motion of objects in their vicinity, particularly for bodies with high area-to-mass ratios. In this work, we adopt the polyhedral gravity model and identify natural dynamical structures that can be used for mission operations. Further, we study forced periodic motion in the body fixed frame while accounting for the effect of SRP with eclipses. Overall, our work seeks to identify suitable orbits and locations in the vicinity of small bodies that can be exploited for the design of science orbits. To obtain periodic orbits in the model accounting for SRP perturbations, we use a Melnikov function to find orbits that satisfy resonances with the asteroid spin and show no net change in energy over the orbit. We then use a differential correction scheme to find numerical solutions in the time-periodic model. Our test cases are potentially hazardous asteroid 101955 Bennu and main belt asteroid 16 Psyche. [ABSTRACT FROM AUTHOR]

This paper investigates the trends of three different species interacting in the same ecosystem. The study is conducted on the ecosystem which consists of a prey S1 and two predators S2 and S3 in such a way that S2 is a predator of S1 and S3 is a predator of both S1 and S2. In addition, S1 and S2 share the same food which is the main food for S1 and the alternative food for S2. A system of three simultaneous nonlinear partial differential equations is used to represent this situation. The local stability of all constant equilibrium points is discussed after showing their feasibility. In addition, a condition for which a coexisting constant equilibrium point is asymptotically globally stable is also investigated. The results showed that the system has eight constant equilibrium points. Five of them are unstable, while the three remaining are asymptotically locally stable under some conditions on the parameters that are involved in the model. [ABSTRACT FROM AUTHOR]

The present paper explores the linear stability of the equilibrium points in the elliptic restricted three-body problem when the more massive primary is oblate and serves as a source of radiation, while the smaller primary is a radiating body. We have investigated the linear stability of these equilibrium points and observed that the collinear ones are unstable, whereas the non-collinear equilibrium points exhibit stability. Additionally, we have analyzed the combined influence of the oblateness parameter and the radiation factors of both primaries, , on the position of equilibrium points. Our observations indicate that as the radiation factor of the more massive primary decreases, the number of equilibrium points increases. [ABSTRACT FROM AUTHOR]

The stability of the transportation system refers to the structural stability of the system. When the system structure is unstable, local or global bifurcation phenomena will occur, which is one of the main reasons for nonlinear traffic phenomena such as congestion. To truly understand the internal mechanism of the formation of these phenomena, it is necessary to analyze the bifurcation of traffic flow. In this paper, the Hopf bifurcation control of a modified viscous macroscopic traffic flow model is studied by using the linear state feedback method, which changes the characteristics of the bifurcation phenomenon of the dynamic system and obtains the required dynamic behavior of the system. First, we can convert the original traffic model into the nonlinear ordinary differential form suitable for bifurcation analysis, solve the equilibrium point of the system, and carry out phase plane analysis. Then, the linear state feedback term is added and the corresponding controlled system is generated, the existence and type of Hopf bifurcation and the existence of saddle node bifurcation are proved. Numerical simulation results show that the analysis and control of Hopf bifurcation in the traffic model are well realized in this paper. [ABSTRACT FROM AUTHOR]

In 2020, J. Sprott proposed a new three dimensional chaotic system with special features such like 1) dissipative and time-reversible; 2) no equilibrium point; 3) lien of initial conditions goes to the attractor. We observed that an extension of the so-called Sprott's 2020 system to four dimensional system with complex dynamics showed either chaotic or hyperchaotic with unbounded orbits. In this paper, a novel five dimensional hyperchaotic system based on Sprott's 2020 system has been proposed. The proposed system shows complex dynamics like hyperchaotic. The proposed system can be classified as a hidden attractor where no equilibrium point appeared or self-excited where an unusual nature of unstable equilibrium points connected to a very complicated function called Lambert W appeared. The dynamical properties of such system are discovered by computing the Lyapunov exponents and bifurcation diagram. Adaptive control to the proposed system was provided. [ABSTRACT FROM AUTHOR]

Copyright of Journal of Ground Improvement is the property of Journal of Ground Improvement Editorial Office and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

In the entire world, pneumonia is one of the leading causes of death, which is particularly dangerous for young children (those under five years old) and the elderly (those over 65). A deterministic susceptible, vaccinated, exposed, infected, and recovered (SVEIR) model is used in this work to mathematically study the dynamics of pneumonia disease and examine stability analysis, basic reproduction numbers, and equilibrium points of dynamical systems theory models. Spatial equilibria are studied to model disease-free equilibria that are locally asymptotic stable. Numerical simulations of the model have been carried out using MATLAB21. The SVEIR flow and its variables for different parameter sets have been studied through numerical simulations. The solution to the issue is provided through the use of illustrated and explicated results. According to research findings, if vaccination rates rise over the necessary vaccination ratio, the sickness will finally vanish from the community. [ABSTRACT FROM AUTHOR]

For several species of microorganisms, a competition model described by a system of nonlinear differential equations with an infinite distributed delay is considered. The asymptotic stability of the equilibrium point corresponding to the survival of only one species and extinction of the others is studied. Conditions on the initial species population sizes and the initial nutrient concentration are indicated under which the system reaches the equilibrium. Additionally, the stabilization rate is estimated. The results are obtained using a Lyapunov–Krasovskii functional. [ABSTRACT FROM AUTHOR]

The objectives of this study are to develop the SEIR model for COVID-19 and evaluate its main parameters such as therapeutic vaccines, vaccination rate, and effectiveness of prophylactic. Global and local stability of the model and numerical simulation are examined. The local stability of equilibrium points was classified. A Lyapunov function is constructed to analyze the global stability of the disease-free equilibrium. The simulation part is based on two situations, including the USA and Iran. Our results provide a good contribution to the current research on this topic. [ABSTRACT FROM AUTHOR]

To theoretically and experimentally characterize the neuronal burst patterns, a simplified FitzHugh–Nagumo (FHN) circuit is developed by using two anti-parallel diodes to achieve nonlinearity, and its non-autonomous system model is thereby built. The simplified FHN system has a time-varying equilibrium point, whose position and stability change slowly over time. By employing numerical measures, periodic and quasi-periodic burst patterns along with quasi-periodic spike patterns are revealed in the simplified FHN system. Particularly, through constructing Hopf bifurcation set, the bifurcation mechanism for the burst behaviors is expounded theoretically. As a result, transitions between the spike and resting states are demonstrated, and Hopf/Hopf periodic and quasi-periodic burst patterns are identified. Finally, with the developed Multisim simulation model, analog circuit simulations and breadboard experiments are performed to confirm numerical results. Notably, the simplified FHN circuit is implemented with low-cost and no multiplier, which is of great significance for the construction of neuromorphic systems and contributes to the research and development of artificial neural networks. [ABSTRACT FROM AUTHOR]

We construct three-dimensional dynamical systems with block-linear discontinuous right-hand side that simulate the simplest molecular oscillators. The phase portrait of each of these systems contains a unique equilibrium point and a cycle lying in the complement of the basin of attraction of this point. There are no other equilibrium points in these phase portraits. [ABSTRACT FROM AUTHOR]

Conventional multi-scroll chaotic systems are often constrained by the number of attractors and the complexity of generation, making it challenging to meet the increasing demands of communication and computation. This paper revolves around the modified Chua’s system. By modifying its differential equation and introducing traditional nonlinear functions, such as the step function sequence and sawtooth function sequence. A nested grid multi-scroll chaotic system (NGMSCS) can be established, capable of generating nested grid multi-scroll attractors. In contrast to conventional grid multi-scroll chaotic attractors, scroll-like phenomena can be initiated outside the grid structure, thereby revealing more complex dynamic behavior and topological features. Through the theoretical design and analysis of the equilibrium point of the system and its stability, the number of saddle-focused equilibrium points of index 2 is further expanded, which can generate (2 N+2) × M attractors, and the formation mechanism is elaborated and verified in detail. In addition, the generation of an arbitrary number of equilibrium points in the y-direction is achieved by transforming the x and y variables, which can generate M×(2 N+2) attractors, increasing the complexity of the system. The system’s dynamical properties are discussed in depth via time series plots, Lyapunov exponents, Poincaré cross sections, 0–1 tests, bifurcation diagrams, and attraction basins. The existence of attractors is confirmed through numerical simulations and FPGA-based hardware experiments.

This mathematical model is based on a system of two non-linear delay differential equations representing GDP (Gross Domestic Product) growth and national debt respectively. Growth of GDP is directly proportional to national debt. In the absence of national debt, there could be no or very slow GDP growth. The national debt is heavily dependent on external loans and external investments. These investments act as a catalyst for accelerating the rate of GDP. It is assumed that the external debt is never paid off fully. The availability of external investments is not immediate as per demand but takes some time for the maturation of the deal. The time delay in actual arrival of the foreign investment and its effect on GDP-National debt dynamics is the main focus of this study. This effect is studied using a delay parameter τ. The non-zero equilibrium of the system is calculated, and the stability analysis is performed on it. Hopf bifurcation is observed for a critical value of the delay parameter. Numerical simulation is performed using MATLAB code.

The tethered asteroid probe system refers to a method of connecting a probe to an asteroid using a tether. This system allows the probe to hover near the asteroid's surface without consuming fuel, making it valuable for conducting high-precision exploration, sampling, and other exploration tasks. However, various physical characteristics, such as the tether length, flexibility, gravity, internal tension, and the initial velocity state of the probe, affect the probe's hovering position and stability. In this article, the dynamic model and stability of tether probes near irregular asteroids are investigated. By considering the mass and elasticity of the tether, a multi-flexible body dynamic equation is established to describe the behavior of the probe and tether under the influence of the gravitational field of the asteroid. Dynamic equations can describe the dynamical response of the probe when switching between the tensed and relaxed states. Moreover, the changes in the position and stability of the stable range caused by the tether are analyzed. The findings suggest that connecting the probe to the asteroid through tethers significantly expands the stable operation range of the probe. The length of the tether and the amplitude of the tension significantly impact the dynamic characteristics of the probe and the stable range. Additionally, compared with the assumption that the tether is assumed to be massless and rigid, the initial range in which the tethered system can be stable is significantly reduced. Hence, the influence of the tether mass, elasticity, and damping should not be overlooked. The research presented in this article holds great significance for asteroid proximity exploration and sampling tasks that utilize tether systems. By understanding the dynamics and stability of tethered probes near irregular asteroids, human capabilities in exploring and studying these celestial bodies can be enhanced. [ABSTRACT FROM AUTHOR]

In this work, two inertial algorithms for approximating common elements of the sets of solutions of three important problems are constructed. The first problem is a generalized mixed equilibrium one involving relaxed monotone mapping, the second is a zero problem of inverse strongly monotone mappings, while the third one is a fixed point problem of a family of relatively nonexpansive mappings. The first algorithm is a shrinking projection type for a common solution of all the three problems. The second is a generalized Alber projection free method for the second and the third problems. Each of the devised algorithms uses the conjugate gradient-like direction, which allows it to accelerate its iterates toward a solution of the problems. The strong convergence theorem for each of the algorithms is formulated and proved in a real 2 - uniformly convex and uniformly smooth Banach space. Additionally, the applications of our algorithms to convex optimization problems and image recovery problems are studied. The advantages and computational efficiency of our methods are analyzed based on their numerical performance in comparison to some of the existing and recently proposed methods using numerical example. [ABSTRACT FROM AUTHOR]

Lotka-Volterra model continues to be of interest to numerous researchers, both in terms of its mathematical development and applications. This paper discusses an analytical solution of the Lotka-Volterra model near its equilibrium point. This solution, which is the main result of this paper, has not been previously explored by other researchers. The proposed solution is in the form of a series expansion with respect to parameter (1), representing a perturbed solution around the equilibrium point. The analytical solution is evaluated by comparing to both the corresponding exact orbit, which is directly derived from the model, and the corresponding numerical solution. Comparisons with the exact orbit reveal that the orbit formed by the analytical solution closely approximates the exact one. The orbits formed by the analytical solution are closer to the exact ones as approaches zero. Similarly, the analytical solution is also closer to the numerical solution as approaches zero. Additionally, as the solutions exhibit wave-like behavior, further observations are made regarding the 'amplitude' and 'wavelength' of the analytical solution. The wavelength and amplitude of the analytical solutions are closer to the ones of the numerical solutions as tends to zero. The amplitude and wavelength are crucial for optimizing harvesting strategies when applying the Lotka-Volterra model in integrated farming systems. [ABSTRACT FROM AUTHOR]

In this paper, a new two-body self-synchronization vibration system characterized by two ideal vibration-exciting motors (asynchronous motors) installed on different vibrating bodies is investigated. Firstly, differential equations of the system are established via the Lagrange equation. Moreover, natural frequencies and stable solutions are obtained. Then, the conditions for the system to implement stable self-synchronization are derived using the equilibrium point theory of the dynamics system and Lyapunov's stability theory. The effects of spring stiffness on the natural frequencies and synchronous motion are numerically analyzed. The steady-state responses of the system are obtained for different structure parameters. The research results show that this system can implement two types of self-synchronization motion under different structure parameters. The first type fluctuates the phase differences in the proximity of zero rad, while the other one fluctuates the phase differences near π rad. Resonance significantly affects the synchronous motion of the system, rapidly changing in phase differences and amplitudes. An increase in the value of k y 2 is not conducive to implementing the stable synchronous motion. Finally, the correctness of the theory and electromechanical coupling simulation results is experimentally validated. The results of this paper can be directly used to determine the structural parameters for a new type of vibrating machine. [ABSTRACT FROM AUTHOR]

A systematic analytical study of the mathematical properties of the previously constructed nonlinear model for shear flow of thixotropic viscoelastic-plastic media is continued. For arbitrary six material parameters and an (increasing) material function that control the model, the basic properties of the families of stress-strain curves at constant strain rates and relaxation curves generated by the model, and the features of the evolution of the structuredness under these types of loading are analytically studied. The dependences of these curves on time, shear rate, initial strain and initial structuredness of the material, as well as on the material parameters and function of the model, are studied. Several indicators of the applicability of the model are found which are convenient to check with experimental data. It was examined what effects typical for viscoelastic-plastic media can be described by the model and what unusual effects (unusual properties) are generated by a change in structuredness in comparison with typical stress-strain curves and relaxation curves of structurally stable materials. In particular, it has been proved that stress-strain curves can be both increasing functions and can have decreasing sections resembling a "yield tooth" or damped oscillations, that all stress-strain curves (SSCs) possess horizontal asymptotes (steady flow stress), monotonically dependent on shear rate, and flow stress increases with shear rate growth, that the instantaneous shear modulus, on the contrary, depends on the initial structuredness, but does not depend on shear rate. Under certain restrictions on the material parameters, the model is also capable of providing a bilinear form of stress-strain curves, which is typical for an ideal elastoplastic model, but with strain rate sensitivity. It has been established that the family of stress-strain curves does not have to be increasing either in initial structuredness or in shear rate: in a certain range of shear rates, in which the equilibrium position is a "mature" focus and pronounced oscillations of stress-strain curves are observed, it is possible to intertwine stress-strain curves with different shear rates. It is proved that for any material parameters and functions, all stress relaxation curves decrease and have a common zero asymptote as time tends to infinity. The analysis proved the ability of the model to describe behavior of not only liquid-like viscoelastoplastic media, but also solid-like (thickening, hardening, hardened) media: creep, relaxation, recovery, a number of typical properties of experimental relaxation curves, creep and stress-strain curves, strain rate and strain hardening, flow under constant stress and so on. [ABSTRACT FROM AUTHOR]

The restricted (N + 1) -vortex problem is investigated in the plane with the first N identical vortices forming a relative equilibrium configuration of a regular N-polygon and the vorticity of the last vortex being zero. We characterize the global dynamics using the method of qualitative theory. It can be shown that the equilibrium points of the system are located at the vertices of three different regular N-polygons and the origin. The equilibrium points on one regular polygon are stable, whereas those on the other two regular polygons are unstable. The origin and singularities are also stable and surrounded by dense periodic orbits. For N = 3 or 4, there exist homoclinic and heteroclinic orbits; while for N ≥ 5 , the system’s orbits consist of equilibrium points, heteroclinic orbits, and periodic orbits. We numerically study the trajectories of the passive tracer (a particle with zero vorticity) under specific circumstances, which support our theoretical results. [ABSTRACT FROM AUTHOR]

The continuous Hopfield network (CHN) has provided a powerful approach to optimization problems and has shown good performance in different domains. However, two primary challenges still remain for this network: defining appropriate parameters and hyperparameters. In this study, our objective is to address these challenges and achieve optimal solutions for combinatorial optimization problems, thereby improving the overall performance of the continuous Hopfield network. To accomplish this, we propose a new technique for tuning the parameters of the CHN by considering its stability. To evaluate our approach, three well-known combinatorial optimization problems, namely, weighted constraint satisfaction problems, task assignment problems, and the traveling salesman problem, were employed. The experiments demonstrate that the proposed approach offers several advantages for CHN parameter tuning and the selection of optimal hyperparameter combinations. [ABSTRACT FROM AUTHOR]

The objective of this study is to establish a dynamical model for the spread of Escherichia coli within a community, while also identifying the key parameters influencing its propagation. Through an in-depth analysis of the dynamical system, two equilibrium points were discerned. Furthermore, the numerical solution of the system revealed the significant impact of various parameters on bacterial dissemination. These parameters encompassed the contact rates among healthy individuals, infected persons, and the bacteria itself. Additionally, the level of compliance with sanitation practices among infected individuals played a pivotal role. Gaining insights into the influence of these parameters holds substantial promise for effectively managing both bacterial spread and associated diseases. [ABSTRACT FROM AUTHOR]

This mathematical model is based on a system of two non-linear delay differential equations representing GDP (Gross Domestic Product) growth and national debt respectively. Growth of GDP is directly proportional to national debt. In the absence of national debt, there could be no or very slow GDP growth. The national debt is heavily dependent on external loans and external investments. These investments act as a catalyst for accelerating the rate of GDP. It is assumed that the external debt is never paid off fully. The availability of external investments is not immediate as per demand but takes some time for the maturation of the deal. The time delay in actual arrival of the foreign investment and its effect on GDP-National debt dynamics is the main focus of this study. This effect is studied using a delay parameter τ. The non-zero equilibrium of the system is calculated, and the stability analysis is performed on it. Hopf bifurcation is observed for a critical value of the delay parameter. Numerical simulation is performed using MATLAB code. [ABSTRACT FROM AUTHOR]

A systematic analytical study of the mathematical properties of the previously constructed nonlinear model of the shear flow of thixotropic viscoelastic-plastic media, which takes into account the mutual influence of the deformation process and structure evolution, is carried out. A set of two nonlinear differential equations describing shear at a constant rate and stress relaxation was obtained. Assuming six material parameters and an (increasing) material function that control the model are arbitrary, the basic properties of the families of stress-strain curves at constant strain rates, stress relaxation curves (Part 2) and creep curves (Part 3) generated by the model, and the features of the evolution of the structuredness under these types of loading were analytically studied. The dependences of these curves on time, shear rate, stress level, initial strain and initial structuredness of material (for example, degree of physical crosslinking), as well as on material parameters and function governing the model, were studied. Several indicators of the model applicability are found, which are convenient to check with experimental data. It was examined what effects typical for viscoelastic-plastic media can be described by the model and what unusual effects (properties) are generated by structuredness changes in comparison to typical stress-strain, relaxation and creep curves of structurally stable materials. The analysis proved the ability of the model to describe behavior of not only liquid-like viscoelastoplastic media, but also solid-like (thickening, hardening, hardened) media: the effects of creep, relaxation, recovery, a number of typical properties of experimental relaxation curves, creep and stress-strain curves at a constant rate, strain rate and strain hardening, flow under constant stress, etc. The first part of the article is devoted to formulation of the model and preparation of basis for the second part: the proof of the uniqueness and stability of the equilibrium point of the nonlinear equations set, analytical study of the equilibrium point dependence on all material parameters, possible types of phase portraits and the properties of integral and phase curves of the model. [ABSTRACT FROM AUTHOR]

Copyright of Journal of Zhengzhou University (Natural Science Edition) is the property of Journal of Zhengzhou University (Natural Science Edition) Editorial Office and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

Tuberculosis has remained the principal cause of mortality worldwide, and one of the major sources of concern is drug-resistant TB. The increasing emergence of extensively drug-resistant and multidrug-resistant TB has further increased the TB epidemic. In this current work, we suggest a model to study the transmission of TB with extensively drug-resistant and multidrug-resistant compartments, incorporating chemoprophylaxis treatment. In the theoretical analysis, the concept of the next-generation matrix and the Jacobian method are applied to obtain a formula that states the reproductive number. The existence of endemic and disease-free equilibrium points was checked, and their stability has been analyzed using the Lyapunov method. The qualitative-based analysis indicated the local asymptotic stability of the disease-free-state for R0 1, whereas the endemic state is globally asymptotically stable if R0 1. Moreover, sensitivity analysis was carefully done using normalized forward sensitivity, and numerical simulation was carried out. Based on the results of numerical simulation and sensitivity analysis, chemoprophylaxis treatment was found to drastically minimize the progression of exposed individuals to infectious classes and also reduce the progression to extensively drug-resistant and multidrug-resistant classes, which decreases disease transmission.

Smart solid-state transformers (STs) have been proposed to modernize the distributed renewable resources dominated distribution system and facilitate the integration of different subsystems/resources as an energy hub/router. A solid power deliver amongst these integrated subsystems is critical to maintain the power balance and to ensure the ST stable operation, while the research on ST loadability analysis is insufficient. Generally, the ST is composed of three-stage offering medium voltage alternative current (MVAC), medium voltage direct current (MVDC), low voltage direct current (LVDC) and low voltage alternative current (LVAC) connectivity. Although the voltage at each port is independently controlled, the power conversion among these ports is electrically coupled and constrained by the maximum deliverable power of each stage. This paper analyzes the operating points of the ST stage by stage with respect to its loadbility and defines the stable operational region of the ST considering the interactions amongst these stages. Moreover, effects of the current limits, voltage regulation and reactive power compensation on the ST loadability and stability enhancement are considered. RT-Lab platform serves to verify the stable operation region of the ST and the efficiency of the above loadability enhancement methods.

In this work, the dynamics of a food chain model with disease in the predator and the Allee effect in the prey have been investigated. The model also incorporates a Holling type-III functional response, accounting for both disease transmission and predation. The existence of equilibria and their stability in the model have also been investigated. The primary objective of this research is to examine the effects of the Allee parameter. Hopf bifurcations are explored about the interior and disease-free equilibrium point, where the Allee is taken as a bifurcation point. In numerical simulation, phase portraits have been used to look into the existence of equilibrium points and their stability. The bifurcation diagrams that have been drawn clearly demonstrate the presence of significant local bifurcations, including Hopf, transcritical, and saddle-node bifurcations. Through the phase portrait, limit cycle, and time series, the stability and oscillatory behaviour of the equilibrium point of the model are investigated. The numerical simulation has been done using MATLAB and Matcont.

As the flexible-controlled power source in the power system, the doubly fed-based variable-speed pumped storage unit (DF-VSPSU) has a significant role in the power rebalance and the reactive power support. However, as with the voltage sag in the remote grid side, the DF-VSPSU with the conventional low-voltage ride-through control may lose the synchronization and result in instability due to the absence of an equilibrium point. Thus, taking a DF-VSPSU infinite system as a case, the generator-side, and the grid-side model is well established. The large disturbance instability mechanism of doubly fed-based variable-speed pumped storage unit under remote grid faults is explained in detail, which is caused by the absence of the equilibrium point. Together with the key influencing factors, including the voltage depth and the short circuit ratio, the available gain of the reactive current control is presented. Finally, the availability of the theoretical analysis is demonstrated based on MATLAB/Simulink.

Overhead contact lines (OCLs) are subjected to longitudinal displacement due to factors such as temperature changes and external force. Excessive longitudinal displacement may prevent the tension balancers from performing their proper tension adjustment function. It is therefore important to develop a method for calculating the longitudinal displacement of OCLs and to make it possible to predict the longitudinal displacement in response to changes in temperature and external forces. This paper presents a model to represent the longitudinal displacement of OCLs on a curved track installing tensioning devices and hinged cantilevers at each support point and proposes calculation methods to find the equilibrium points of the longitudinal displacement of the OCL. Furthermore, the validation of the proposed calculation methods was confirmed by scale model tests.

Under the sharp turn condition, especially on low adhesion coefficient roads, drift motion can improve vehicle agility and ensure safety. During drift motion, the large sideslip angle and rear wheel slip as well as the saturation of lateral tyre force result in the complex nonlinear dynamic behaviour, such as non-unique equilibrium point and unstable vehicle dynamic. Therefore, this paper focuses on the analysis of dynamic characteristics and the design of both the equilibrium point and feedback controller for drift motion. First, a dynamics model, in which the rear wheel slip ratio is treated as a parametric variable and the influence of rear wheel lateral force on the drift motion is explicitly expressed, is established. Then the expression of steady-state yaw rate and the virtual control input is derived, and the error dynamic model is presented furthermore. To design the equilibrium point, in this paper the effect of rear tyre slip angle and slip ratio on the equilibrium point is discussed, and the condition of stable equilibrium point is proposed. In addition, the design of desired rear tyre slip angle by synthesising the cornering performance during drift motion is presented. For the drift controller design, the main idea is to design the stabilisation controller for the nonlinear dynamic system with the stable equilibrium point and to calculate static feedback gain by means of Lyapunov stability theory. To illustrate the characteristics of drift motion, the influence of the vehicle speed and rear wheel slip ratio on the vehicle path and the low damping characteristics of the dynamic system on the control performance are analysed by different simulation conditions. Moreover, the performance and effectiveness of the proposed drift control are verified by simulation. [ABSTRACT FROM AUTHOR]

In this paper we study the discrete-time dynamical systems associated with gonosomal algebras used as algebraic model in the sex-linked genes inheritance. We show that the class of gonosomal algebras is disjoint from the other non-associative algebras usually studied (Lie, alternative, Jordan, associative power). To each gonosomal algebra, with the mapping x ↦ 1 2 x 2 , an evolution operator W is associated that gives the state of the offspring population at the birth stage, then from W we define the operator V which gives the frequency distribution of genetic types. We study discrete-time dynamical systems generated by these two operators, in particular we show that the various stability notions of the equilibrium points are preserved by passing from W to V. Moreover, for the evolution operators associated with genetic disorders in the case of a diallelic gonosomal lethal gene we give complete analysis of fixed and limit points of the dynamical systems. [ABSTRACT FROM AUTHOR]

The dissemination of hate speech has become an issue of great concern. Hate speech not only undermines social harmony but also poses significant challenges to the smooth functioning of the public sector and the well-being of the community members. In this study, we formulated and analyzed a Caputo fractional order model with optimal control strategies on the dissemination of hate speech, as an evolutionary system. The non-negativity and boundedness of the solutions of the fractional order model have been shown to make the evolutionary system meaningful. Both the hate speech-free and hate speech-persistent equilibrium points were determined. Conditions for the backward bifurcation of the fractional order model were analyzed when the effective reproduction number of the hate speech model is less than unity. The global asymptotic stability of the hate speech-persistent equilibrium point has also been shown. Moreover, we employed Pontryagin's Maximum Principle to determine the optimality conditions of the optimal control problem, performed sensitivity analysis on the model parameters, and conducted numerical simulations using MATLAB's ode45 solver in combination with Euler's forward and backward numerical methods. This enabled us to investigate the effects of order of the fractional derivative and the proposed strategies on the behavior of responses of the model. Implementing protection and treatment strategies against hate speech dissemination has a significant effect on disrupting and counteracting the propagation of hate speeches within a community, as evidenced by the graphical representation of the numerical simulation. [ABSTRACT FROM AUTHOR]

Due to the lack of timely protection measures against infectious diseases, or based on the particularity of the transmission of some infectious diseases and the time-varying connections between people, the transmission dynamics of infectious diseases in the information society are becoming more and more complex and changeable. A fractional-order epidemic mathematical model with network weighting and latency is proposed in this paper, and the stability near the disease-free equilibrium point and endemic equilibrium point are discussed separately. Subsequently, an event-triggered impulsive control strategy based on an infection rate threshold is put forward. By selecting the appropriate control gain, the Zeno phenomenon can be eliminated on the premise of ensuring the stability of the control error system. Finally, the theoretical results were validated numerically and some conclusions are presented. These findings contribute to future research on the limited-time event-triggered impulsive control of infectious diseases. [ABSTRACT FROM AUTHOR]

In this paper, an adaptive predictive control for controlling and stabilizing fractional order chaotic systems around the equilibrium point is provided. The stability of fractional order chaotic systems around equilibrium points in the presence of parameter uncertainty has been demonstrated using Lyapunov's stability theorem. In addition, the uncertain parameters of fractional order chaotic systems are calculated using appropriate adaptive methods based on the proposed predictive controller structure. Rossler and Chen systems were considered to numerical simulations. The results demonstrated the adaptive predictive control method's usefulness and performance. [ABSTRACT FROM AUTHOR]