Pub Date : 2020-08-14DOI: 10.1504/ijdsde.2020.10031333
Amina Feddaoui, J. Llibre, A. Makhlouf
The averaging theory of second order shows that for polynomial differential systems in ℝ4 with cubic homogeneous nonlinearities at least nine limit cycles can be born in a zero-Hopf bifurcation.
二阶平均理论表明ℝ4具有三次齐次非线性，在零Hopf分岔中可以产生至少九个极限环。
{"title":"4-dimensional zero-Hopf bifurcation for polynomial differentials systems with cubic homogeneous nonlinearities via averaging theory","authors":"Amina Feddaoui, J. Llibre, A. Makhlouf","doi":"10.1504/ijdsde.2020.10031333","DOIUrl":"https://doi.org/10.1504/ijdsde.2020.10031333","url":null,"abstract":"The averaging theory of second order shows that for polynomial differential systems in ℝ4 with cubic homogeneous nonlinearities at least nine limit cycles can be born in a zero-Hopf bifurcation.","PeriodicalId":43101,"journal":{"name":"International Journal of Dynamical Systems and Differential Equations","volume":null,"pages":null},"PeriodicalIF":0.3,"publicationDate":"2020-08-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"49667119","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2020-08-14DOI: 10.1504/ijdsde.2020.10031334
Rakesh Kumar, A. Sharma, K. Agnihotri
A nonlinear form of Bass model for innovation diffusion consisting of a system of two variables viz. for adopters and nonadopters population is proposed to lay stress on the evaluation period. The local stability of a positive equilibrium and the existence of Hopf bifurcation are demonstrated by analysing the associated characteristic equation. The critical value of evaluation period is determined beyond which small amplitude oscillations of the adopter and nonadopters population occur, and this critical value goes on decreasing with the increase in carrying capacity of the non-adopters population. The direction and the stability of bifurcating periodic solutions is determined by using the normal form theory and centre manifold theorem. It is observed that the cumulative density of external influences has a significant role in developing the maturity stage (final adoption stage) in the system. Numerical computations are executed to confirm the correctness of theoretical investigations.
{"title":"Bifurcation behaviour of a nonlinear innovation diffusion model with external influences","authors":"Rakesh Kumar, A. Sharma, K. Agnihotri","doi":"10.1504/ijdsde.2020.10031334","DOIUrl":"https://doi.org/10.1504/ijdsde.2020.10031334","url":null,"abstract":"A nonlinear form of Bass model for innovation diffusion consisting of a system of two variables viz. for adopters and nonadopters population is proposed to lay stress on the evaluation period. The local stability of a positive equilibrium and the existence of Hopf bifurcation are demonstrated by analysing the associated characteristic equation. The critical value of evaluation period is determined beyond which small amplitude oscillations of the adopter and nonadopters population occur, and this critical value goes on decreasing with the increase in carrying capacity of the non-adopters population. The direction and the stability of bifurcating periodic solutions is determined by using the normal form theory and centre manifold theorem. It is observed that the cumulative density of external influences has a significant role in developing the maturity stage (final adoption stage) in the system. Numerical computations are executed to confirm the correctness of theoretical investigations.","PeriodicalId":43101,"journal":{"name":"International Journal of Dynamical Systems and Differential Equations","volume":null,"pages":null},"PeriodicalIF":0.3,"publicationDate":"2020-08-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43206718","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2020-08-14DOI: 10.1504/ijdsde.2020.10031331
R. Rach, Jun-Sheng Duan, A. Wazwaz
In this work, we use the Adomian decomposition method to study large deflections of a flexible cantilever beam fabricated from functionally graded materials with a sinusoidal nonlinearity. We convert the specified nonlinear boundary value problem with Dirichlet and Neumann boundary conditions, that governs the large deflections, to an equivalent nonlinear Fredholm-Volterra integral equation. We illustrate the obtained approximations by appropriate graphs and examine the resulting possible errors. Finally, we discuss the relationship of the deflection and the model parameters.
{"title":"Simulation of large deflections of a flexible cantilever beam fabricated from functionally graded materials by the Adomian decomposition method","authors":"R. Rach, Jun-Sheng Duan, A. Wazwaz","doi":"10.1504/ijdsde.2020.10031331","DOIUrl":"https://doi.org/10.1504/ijdsde.2020.10031331","url":null,"abstract":"In this work, we use the Adomian decomposition method to study large deflections of a flexible cantilever beam fabricated from functionally graded materials with a sinusoidal nonlinearity. We convert the specified nonlinear boundary value problem with Dirichlet and Neumann boundary conditions, that governs the large deflections, to an equivalent nonlinear Fredholm-Volterra integral equation. We illustrate the obtained approximations by appropriate graphs and examine the resulting possible errors. Finally, we discuss the relationship of the deflection and the model parameters.","PeriodicalId":43101,"journal":{"name":"International Journal of Dynamical Systems and Differential Equations","volume":null,"pages":null},"PeriodicalIF":0.3,"publicationDate":"2020-08-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42830076","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2020-06-16DOI: 10.1504/ijdsde.2020.10030020
Yizhong Liu
This paper is concerned with chaos control for a modified Sprott E system. Applying time-delayed feedback control method, we establish some new conditions to control chaotic behaviour of modified Sprott E system. With the aid of local stability analysis, we theoretically prove the occurrences of Hopf bifurcation. Computer simulations are implemented to support analytical results. Finally, a brief conclusion is included.
{"title":"Time feedback control in a modified Sprott E model","authors":"Yizhong Liu","doi":"10.1504/ijdsde.2020.10030020","DOIUrl":"https://doi.org/10.1504/ijdsde.2020.10030020","url":null,"abstract":"This paper is concerned with chaos control for a modified Sprott E system. Applying time-delayed feedback control method, we establish some new conditions to control chaotic behaviour of modified Sprott E system. With the aid of local stability analysis, we theoretically prove the occurrences of Hopf bifurcation. Computer simulations are implemented to support analytical results. Finally, a brief conclusion is included.","PeriodicalId":43101,"journal":{"name":"International Journal of Dynamical Systems and Differential Equations","volume":null,"pages":null},"PeriodicalIF":0.3,"publicationDate":"2020-06-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42142531","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2020-06-16DOI: 10.1504/ijdsde.2020.10030019
Xianmin Zhang
In this paper, the non-uniqueness of solution is mainly considered to the initial value problem (IVP) for the system of impulsive fractional differential equations (IFrDE) with Caputo-Katugampola derivative. The IVP for IFrDE with Caputo-Katugampola derivative is equivalent to the integral equations with an arbitrary constant, which means that the solution is non-unique. Finally, a numerical example is provided to show the main result.
{"title":"Non-uniqueness of solution for initial value problem of impulsive Caputo-Katugampola fractional differential equations","authors":"Xianmin Zhang","doi":"10.1504/ijdsde.2020.10030019","DOIUrl":"https://doi.org/10.1504/ijdsde.2020.10030019","url":null,"abstract":"In this paper, the non-uniqueness of solution is mainly considered to the initial value problem (IVP) for the system of impulsive fractional differential equations (IFrDE) with Caputo-Katugampola derivative. The IVP for IFrDE with Caputo-Katugampola derivative is equivalent to the integral equations with an arbitrary constant, which means that the solution is non-unique. Finally, a numerical example is provided to show the main result.","PeriodicalId":43101,"journal":{"name":"International Journal of Dynamical Systems and Differential Equations","volume":null,"pages":null},"PeriodicalIF":0.3,"publicationDate":"2020-06-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44510085","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2020-06-16DOI: 10.1504/ijdsde.2020.10030022
Ashraf M. A. Ahmad, Y. A. Hour, M. DarAssi
The removable devices (RD) is one of the important factors that affects the virus spreading. We assumed that the infected RD could affect the nodes of S and E compartments at the rates, θ1 and θ2, respectively. While the previous studies considered this effect on susceptible compartment only. Moreover, we considered the effect of the rate of the nodes which are break down from network because of infected RD, μ1. This model has no virus-free equilibrium and has a unique endemic equilibrium. The theorems of asymptotically autonomous systems and the generalised Poincare-Bendixson are used to show that the endemic equilibrium is globally asymptotically stable. Numerical methods are used to solve the obtained system of differential equations and the solutions are illustrated in several examples. The effects of ξ, ϵ, θ1 and θ2 rates on the devices that moved from latent to recovered nodes are investigated.
{"title":"Effects of computer networks' viruses under the of removable devices","authors":"Ashraf M. A. Ahmad, Y. A. Hour, M. DarAssi","doi":"10.1504/ijdsde.2020.10030022","DOIUrl":"https://doi.org/10.1504/ijdsde.2020.10030022","url":null,"abstract":"The removable devices (RD) is one of the important factors that affects the virus spreading. We assumed that the infected RD could affect the nodes of S and E compartments at the rates, θ1 and θ2, respectively. While the previous studies considered this effect on susceptible compartment only. Moreover, we considered the effect of the rate of the nodes which are break down from network because of infected RD, μ1. This model has no virus-free equilibrium and has a unique endemic equilibrium. The theorems of asymptotically autonomous systems and the generalised Poincare-Bendixson are used to show that the endemic equilibrium is globally asymptotically stable. Numerical methods are used to solve the obtained system of differential equations and the solutions are illustrated in several examples. The effects of ξ, ϵ, θ1 and θ2 rates on the devices that moved from latent to recovered nodes are investigated.","PeriodicalId":43101,"journal":{"name":"International Journal of Dynamical Systems and Differential Equations","volume":null,"pages":null},"PeriodicalIF":0.3,"publicationDate":"2020-06-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"41343736","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2020-06-16DOI: 10.1504/ijdsde.2020.10030021
Hui Li, Yige Zhao, Shurong Sun
This paper is dedicated to discussing the oscillation of the second order neutral delay differential equations (r(t)(z´(t))α)´ + q(t)f(xβ(σ(t))) = 0, where z(t) = x(t) + p(t)x(τ(t)). Sufficient conditions are provided by Riccati transformation comparing with related first order differential inequalities and differential equations. Results obtained in this paper have extended and improved conclusions contained in other literatures. Several illustrative examples are presented.
{"title":"Oscillation of one kind of second order neutral delay differential equations","authors":"Hui Li, Yige Zhao, Shurong Sun","doi":"10.1504/ijdsde.2020.10030021","DOIUrl":"https://doi.org/10.1504/ijdsde.2020.10030021","url":null,"abstract":"This paper is dedicated to discussing the oscillation of the second order neutral delay differential equations (r(t)(z´(t))α)´ + q(t)f(xβ(σ(t))) = 0, where z(t) = x(t) + p(t)x(τ(t)). Sufficient conditions are provided by Riccati transformation comparing with related first order differential inequalities and differential equations. Results obtained in this paper have extended and improved conclusions contained in other literatures. Several illustrative examples are presented.","PeriodicalId":43101,"journal":{"name":"International Journal of Dynamical Systems and Differential Equations","volume":null,"pages":null},"PeriodicalIF":0.3,"publicationDate":"2020-06-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44267449","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2020-03-18DOI: 10.1504/ijdsde.2020.106028
Halima Atitallah, A. Aribi, M. Aoun
In this paper, two model-based methods are considered for the diagnosis of time-delay fractional systems. Time-delay fractional Luenberger observer without unknown input and time-delay fractional unknown input observer are developed and used for fault detection and isolation. A single observer scheme is needed for fault detection and a bank of generalized (respectively dedicated) observers is required for fault isolation. A theoretical study investigating the convergence condition for each observer-based method in terms of matrix inequalities is presented. Residual sensitivities to faults and to disturbances are studied. Time-delay fractional unknown input observer parameters are computed to obtain structured residuals. This observer ensures unknown input decoupling from the state which results residual insensitive to unknown inputs. Two numerical examples to validate the efficiency of the proposed approaches are given.
{"title":"Diagnosis of time-delay fractional systems using observer-based methods","authors":"Halima Atitallah, A. Aribi, M. Aoun","doi":"10.1504/ijdsde.2020.106028","DOIUrl":"https://doi.org/10.1504/ijdsde.2020.106028","url":null,"abstract":"In this paper, two model-based methods are considered for the diagnosis of time-delay fractional systems. Time-delay fractional Luenberger observer without unknown input and time-delay fractional unknown input observer are developed and used for fault detection and isolation. A single observer scheme is needed for fault detection and a bank of generalized (respectively dedicated) observers is required for fault isolation. A theoretical study investigating the convergence condition for each observer-based method in terms of matrix inequalities is presented. Residual sensitivities to faults and to disturbances are studied. Time-delay fractional unknown input observer parameters are computed to obtain structured residuals. This observer ensures unknown input decoupling from the state which results residual insensitive to unknown inputs. Two numerical examples to validate the efficiency of the proposed approaches are given.","PeriodicalId":43101,"journal":{"name":"International Journal of Dynamical Systems and Differential Equations","volume":null,"pages":null},"PeriodicalIF":0.3,"publicationDate":"2020-03-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1504/ijdsde.2020.106028","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47047154","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2020-03-18DOI: 10.1504/ijdsde.2020.106029
Yunhong Li, Weihua Jiang
In this paper, the existence of multiple positive solutions is considered for nonlinear three-point problem for Riemann-Liouville fractional differential equation. We use the Avery-Peterson fixed point theorem to acquire the existence of multiple positive solutions for the boundary value problem. Two examples are also presented to illustrate the effectiveness of the main result.
{"title":"Existence of multiple positive solutions for nonlinear three-point problem for Riemann-Liouville fractional differential equation","authors":"Yunhong Li, Weihua Jiang","doi":"10.1504/ijdsde.2020.106029","DOIUrl":"https://doi.org/10.1504/ijdsde.2020.106029","url":null,"abstract":"In this paper, the existence of multiple positive solutions is considered for nonlinear three-point problem for Riemann-Liouville fractional differential equation. We use the Avery-Peterson fixed point theorem to acquire the existence of multiple positive solutions for the boundary value problem. Two examples are also presented to illustrate the effectiveness of the main result.","PeriodicalId":43101,"journal":{"name":"International Journal of Dynamical Systems and Differential Equations","volume":null,"pages":null},"PeriodicalIF":0.3,"publicationDate":"2020-03-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1504/ijdsde.2020.106029","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"41717273","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2020-03-18DOI: 10.1504/ijdsde.2020.106025
Binayak Nath, K. Das
The paper explores a tri-trophic food chain model with harvesting in the species. The curiosity of this paper is to observe chaotic dynamics and its control. We perform the local stability analysis of the equilibrium points. The Hopf bifurcation analysis and global stability around the interior equilibrium point are also performed. Our numerical simulations reveal that the three species food chain model induces chaos from period-doubling, limit cycle and stable focus for increasing values of half saturation constant. We conclude that chaotic dynamics can be controlled by the harvesting parameter. We apply basic tools of non-linear dynamics such as Poincare section and Lyapunov exponent to identify chaotic behaviour of the system.
{"title":"Harvesting in tri-trophic food chain stabilises the chaotic dynamics-conclusion drawn from Hastings and Powell model","authors":"Binayak Nath, K. Das","doi":"10.1504/ijdsde.2020.106025","DOIUrl":"https://doi.org/10.1504/ijdsde.2020.106025","url":null,"abstract":"The paper explores a tri-trophic food chain model with harvesting in the species. The curiosity of this paper is to observe chaotic dynamics and its control. We perform the local stability analysis of the equilibrium points. The Hopf bifurcation analysis and global stability around the interior equilibrium point are also performed. Our numerical simulations reveal that the three species food chain model induces chaos from period-doubling, limit cycle and stable focus for increasing values of half saturation constant. We conclude that chaotic dynamics can be controlled by the harvesting parameter. We apply basic tools of non-linear dynamics such as Poincare section and Lyapunov exponent to identify chaotic behaviour of the system.","PeriodicalId":43101,"journal":{"name":"International Journal of Dynamical Systems and Differential Equations","volume":null,"pages":null},"PeriodicalIF":0.3,"publicationDate":"2020-03-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1504/ijdsde.2020.106025","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48275912","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
京公网安备 11010802042870号
京ICP备2023020795号-1
扫码关注我们
求助内容：
应助结果提醒方式：