A three species food web model involving a stage structure and cannibalism in the top predator sp... more A three species food web model involving a stage structure and cannibalism in the top predator species is proposed and studied. It is assumed that the prey species growth logistically in the absence of predator and the predation process occurred according to theLotka-Volterra functional response. The existence, uniqueness and bounded-ness of the solution of the model are investigated. The local and global stability conditions of all possible equilibrium points are established.The persistence conditions of the model are also determined. The local bifurcation near each of the equilibrium points is analyzed. The global dynamics of the model is investigated numerically and compared with the obtained analytical results. It is observed that the proposed model is sensitive to changing in the parameter's values.
In this paper, a four species mathematical models involving different types of ecological interac... more In this paper, a four species mathematical models involving different types of ecological interactions is proposed and analyzed. Holling type – II functional response is a doubted to describes the behavior of predation. The existence, uniqueness and boundedness of the solution are discussed. The existences and the stability analysis of all possible equilibrium points are studied. suitable Lyapunov functions are used to study the global dynamics of the system. Numerical simulations are also carried out to investigate the influence of certain parameters on the dynamical behavior of the model, to support the analytical results of the model.
In this paper, the aquatic food chain model, consisting of Phytoplankton, Zooplankton, and F... more In this paper, the aquatic food chain model, consisting of Phytoplankton, Zooplankton, and Fish, in the contaminated environment is proposed and studied. Modified Leslie–Gower model with Holling type IV functional response are used to describe the growth of Fish and the food transition throughout the food chain, respectively. The toxic substance affects directly the Phytoplankton and indirectly the other species. The local stability analysis of all possible equilibrium points is done. The persistence conditions of the model are established. The basin of attraction for each point is specified using the Lyapunov function. Bifurcation analysis near the coexistence equilibrium point is investigated. Detecting the existence of chaos is carried out using bifurcation diagrams. Numerical simulation shows that the food chain has rich dynamics including chaos. Moreover, the existence of toxic substances works as a stabilizing factor in the model.
A prey–predator interaction model has been suggested in which the population of a predator consis... more A prey–predator interaction model has been suggested in which the population of a predator consists of a two-stage structure. Modified Holling’s disk equation is used to describe the consumption of the prey so that it involves the additional source of food for the predator. The fear function is imposed on prey. It is supposed that the prey exhibits anti-predator behavior and may kill the adult predator due to their struggle against predation. The proposed model is investigated for existence, uniqueness, and boundedness. After determining all feasible equilibrium points, the local stability analyses are performed. In addition, global stability analyses for this model using the Lyapunov method are investigated. The chance of occurrence of local bifurcation including Hopf bifurcation is investigated. Furthermore, to complete our study, the global dynamics of the model are investigated and the set of control parameters is set by conducting numerical simulations.
In this paper the dynamics of bilharazia disease in the humans, which represents its main host, i... more In this paper the dynamics of bilharazia disease in the humans, which represents its main host, is formulated mathematically. The proposed system is studied analytically. The local stability is investigated for all possible equilibrium points. Using suitable Lyapunov functions the basin of attraction of each point is specified. The conditions of occurring local bifurcation in the system are established. Numerical simulations are performed to study the global dynamics of the system and specify the set of control parameters. It is observed that the system has no periodic dynamics and the disease is controlled under some conditions on the parameters. Keywords : Bilharzia; Parasite disease; Stability; Local bifurcation.
An epidemic model that describes the dynamics of the spread of infectious diseases is proposed. T... more An epidemic model that describes the dynamics of the spread of infectious diseases is proposed. Two different types of infectious diseases that spread through both horizontal and vertical transmission in the host population are considered. The basic reproduction numberR0is determined. The local and the global stability of all possible equilibrium points are achieved. The local bifurcation analysis and Hopf bifurcation analysis for the four-dimensional epidemic model are studied. Numerical simulations are used to confirm our obtained analytical results.
A partial temporary immunity SIR epidemic model involv nonlinear treatment rate is proposed ... more A partial temporary immunity SIR epidemic model involv nonlinear treatment rate is proposed and studied. The basic reproduction number is determined. The local and global stability of all equilibria of the model are analyzed. The conditions for occurrence of local bifurcation in the proposed epidemic model are established. Finally, numerical simulation is used to confirm our obtained analytical results and specify the control set of parameters that affect the dynamics of the model.
Abstract In this paper, we established a mathematical model of an S I 1 I 2 R epidemic disease wi... more Abstract In this paper, we established a mathematical model of an S I 1 I 2 R epidemic disease with saturated incidence and general recovery functions of the first disease I 1 . Considering the basic reproduction number, we obtained conditions for both disease-free and co-existing cases. The equilibrium points local stability is verified by using the Routh-Hurwitz criterion, while for the global stability, we used a suitable Lyapunov function to analyze the endemic spread of the positive equilibrium point. Moreover, we carried out the local bifurcation around both equilibrium points (disease-free and co-existing), where we obtained that the disease-free equilibrium point undergoes a transcritical bifurcation. We conduct numerical simulations that supported our theoretical findings.
A modified Leslie-Gower predator-prey model with fear effect and nonlinear harvesting is develope... more A modified Leslie-Gower predator-prey model with fear effect and nonlinear harvesting is developed and investigated in this study. The predator is supposed to feed on the prey using Holling type-II functional response. The goal is to see how fear of predation and presence of harvesting affect the model's dynamics. The system's positivity and boundlessness are demonstrated. All conceivable equilibria's existence and stability requirements are established. All sorts of local bifurcation occurrence conditions are presented. Extensive numerical simulations of the proposed model are shown in form of Phase portraits and direction fields. That is to guarantee the correctness of the theoretical results of the dynamic behavior of the system and to confirm the existence of various forms of bifurcations. The fear rate is observed to have a stabilizing effect up to a threshold value, after which it leads to prey extinction. The harvesting coefficients, on the other hand, serve as co...
Texture classification is the process to classify different textures from the given images. It is... more Texture classification is the process to classify different textures from the given images. It is implemented in a large variety of real world problems involving specific textures of different objects. Some of the real world applications that involve textured objects of surfaces include rock classification, wood species recognition, face detection, fabric classification, geographical landscape segmentation, etc. All these applications allowed the target subjects to be viewed as a specific type of texture and hence, they can be solved using texture classification techniques. Due to this variety of applications, there is a variety in the texture types and every type has to be treated carefully according to its significant properties. Feature extraction is an important process for texture classification. This work introduces several sets of feature according to the type of texture. Three types of textures (datasets) were studied; dataset#1 consists of gray texture with directional prop...
A three species food web model involving a stage structure and cannibalism in the top predator sp... more A three species food web model involving a stage structure and cannibalism in the top predator species is proposed and studied. It is assumed that the prey species growth logistically in the absence of predator and the predation process occurred according to theLotka-Volterra functional response. The existence, uniqueness and bounded-ness of the solution of the model are investigated. The local and global stability conditions of all possible equilibrium points are established.The persistence conditions of the model are also determined. The local bifurcation near each of the equilibrium points is analyzed. The global dynamics of the model is investigated numerically and compared with the obtained analytical results. It is observed that the proposed model is sensitive to changing in the parameter's values.
In this paper, a four species mathematical models involving different types of ecological interac... more In this paper, a four species mathematical models involving different types of ecological interactions is proposed and analyzed. Holling type – II functional response is a doubted to describes the behavior of predation. The existence, uniqueness and boundedness of the solution are discussed. The existences and the stability analysis of all possible equilibrium points are studied. suitable Lyapunov functions are used to study the global dynamics of the system. Numerical simulations are also carried out to investigate the influence of certain parameters on the dynamical behavior of the model, to support the analytical results of the model.
In this paper, the aquatic food chain model, consisting of Phytoplankton, Zooplankton, and F... more In this paper, the aquatic food chain model, consisting of Phytoplankton, Zooplankton, and Fish, in the contaminated environment is proposed and studied. Modified Leslie–Gower model with Holling type IV functional response are used to describe the growth of Fish and the food transition throughout the food chain, respectively. The toxic substance affects directly the Phytoplankton and indirectly the other species. The local stability analysis of all possible equilibrium points is done. The persistence conditions of the model are established. The basin of attraction for each point is specified using the Lyapunov function. Bifurcation analysis near the coexistence equilibrium point is investigated. Detecting the existence of chaos is carried out using bifurcation diagrams. Numerical simulation shows that the food chain has rich dynamics including chaos. Moreover, the existence of toxic substances works as a stabilizing factor in the model.
A prey–predator interaction model has been suggested in which the population of a predator consis... more A prey–predator interaction model has been suggested in which the population of a predator consists of a two-stage structure. Modified Holling’s disk equation is used to describe the consumption of the prey so that it involves the additional source of food for the predator. The fear function is imposed on prey. It is supposed that the prey exhibits anti-predator behavior and may kill the adult predator due to their struggle against predation. The proposed model is investigated for existence, uniqueness, and boundedness. After determining all feasible equilibrium points, the local stability analyses are performed. In addition, global stability analyses for this model using the Lyapunov method are investigated. The chance of occurrence of local bifurcation including Hopf bifurcation is investigated. Furthermore, to complete our study, the global dynamics of the model are investigated and the set of control parameters is set by conducting numerical simulations.
In this paper the dynamics of bilharazia disease in the humans, which represents its main host, i... more In this paper the dynamics of bilharazia disease in the humans, which represents its main host, is formulated mathematically. The proposed system is studied analytically. The local stability is investigated for all possible equilibrium points. Using suitable Lyapunov functions the basin of attraction of each point is specified. The conditions of occurring local bifurcation in the system are established. Numerical simulations are performed to study the global dynamics of the system and specify the set of control parameters. It is observed that the system has no periodic dynamics and the disease is controlled under some conditions on the parameters. Keywords : Bilharzia; Parasite disease; Stability; Local bifurcation.
An epidemic model that describes the dynamics of the spread of infectious diseases is proposed. T... more An epidemic model that describes the dynamics of the spread of infectious diseases is proposed. Two different types of infectious diseases that spread through both horizontal and vertical transmission in the host population are considered. The basic reproduction numberR0is determined. The local and the global stability of all possible equilibrium points are achieved. The local bifurcation analysis and Hopf bifurcation analysis for the four-dimensional epidemic model are studied. Numerical simulations are used to confirm our obtained analytical results.
A partial temporary immunity SIR epidemic model involv nonlinear treatment rate is proposed ... more A partial temporary immunity SIR epidemic model involv nonlinear treatment rate is proposed and studied. The basic reproduction number is determined. The local and global stability of all equilibria of the model are analyzed. The conditions for occurrence of local bifurcation in the proposed epidemic model are established. Finally, numerical simulation is used to confirm our obtained analytical results and specify the control set of parameters that affect the dynamics of the model.
Abstract In this paper, we established a mathematical model of an S I 1 I 2 R epidemic disease wi... more Abstract In this paper, we established a mathematical model of an S I 1 I 2 R epidemic disease with saturated incidence and general recovery functions of the first disease I 1 . Considering the basic reproduction number, we obtained conditions for both disease-free and co-existing cases. The equilibrium points local stability is verified by using the Routh-Hurwitz criterion, while for the global stability, we used a suitable Lyapunov function to analyze the endemic spread of the positive equilibrium point. Moreover, we carried out the local bifurcation around both equilibrium points (disease-free and co-existing), where we obtained that the disease-free equilibrium point undergoes a transcritical bifurcation. We conduct numerical simulations that supported our theoretical findings.
A modified Leslie-Gower predator-prey model with fear effect and nonlinear harvesting is develope... more A modified Leslie-Gower predator-prey model with fear effect and nonlinear harvesting is developed and investigated in this study. The predator is supposed to feed on the prey using Holling type-II functional response. The goal is to see how fear of predation and presence of harvesting affect the model's dynamics. The system's positivity and boundlessness are demonstrated. All conceivable equilibria's existence and stability requirements are established. All sorts of local bifurcation occurrence conditions are presented. Extensive numerical simulations of the proposed model are shown in form of Phase portraits and direction fields. That is to guarantee the correctness of the theoretical results of the dynamic behavior of the system and to confirm the existence of various forms of bifurcations. The fear rate is observed to have a stabilizing effect up to a threshold value, after which it leads to prey extinction. The harvesting coefficients, on the other hand, serve as co...
Texture classification is the process to classify different textures from the given images. It is... more Texture classification is the process to classify different textures from the given images. It is implemented in a large variety of real world problems involving specific textures of different objects. Some of the real world applications that involve textured objects of surfaces include rock classification, wood species recognition, face detection, fabric classification, geographical landscape segmentation, etc. All these applications allowed the target subjects to be viewed as a specific type of texture and hence, they can be solved using texture classification techniques. Due to this variety of applications, there is a variety in the texture types and every type has to be treated carefully according to its significant properties. Feature extraction is an important process for texture classification. This work introduces several sets of feature according to the type of texture. Three types of textures (datasets) were studied; dataset#1 consists of gray texture with directional prop...
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