Search Results - Difference and functional equations Difference equations Bifurcation theory

Mathematics of continuous and discrete dynamical systems : AMS special session in honor of Ronald Mickens's 70th birthday nonstandard finite-difference discretizations and nonlinear oscillations, January 9-10, 2013, San Diego, CA by Gumel, Abba B., AMS Special Session in Honor of Ronald Mickens's 70th Birthday, Nonstandard Finite-Difference Discretizations and Nonlinear Oscillations

“… finite-difference methods for solving continuous-time ordinary and partial differential equation models, the analytical and numerical study of models that undergo nonlinear oscillations, as well…”
Get full text

Bifurcations, chaotic behavior, sensitivity analysis, and various soliton solutions for the extended nonlinear Schrödinger equation by ur Rahman, Mati, Sun, Mei, Boulaaras, Salah, Baleanu, Dumitru

“… We then employ principles from planar dynamical systems theory to explore the bifurcation phenomena exhibited within this derived system…”
Get full text

Stability and Neimark–Sacker Bifurcation of Certain Mixed Monotone Rational Second-Order Difference Equation by Nurkanović, Zehra, Nurkanović, Mehmed, Garić-Demirović, Mirela

“…This paper investigates the local and global character of the unique positive equilibrium of certain mixed monotone rational second-order difference equation with quadratic terms…”
Get full text

Stability and Hopf bifurcation of a predator-prey model with Smith growth rate and Monod–Haldane functional response by Feng, Xiaozhou, Li, Kunyu, Liu, Mengyan, Wang, Lin, Wang, Tonghui

“… Then considering the non-uniform distribution of populations in nature, by standard linear operator theory and center manifold theorem, the Turing instability and the Hopf bifurcation of the PDE…”
Get full text

Chaos, control, and synchronization in some fractional-order difference equations by Khennaoui, Amina-Aicha, Ouannas, Adel, Bendoukha, Samir, Grassi, Giuseppe, Wang, Xiong, Pham, Viet-Thanh, Alsaadi, Fawaz E.

“…, Rössler, and Wang maps. The dynamics of the proposed fractional maps are investigated experimentally by means of phase portraits, bifurcation diagrams, and Lyapunov exponents…”
Get full text

Combinatorial perturbation analysis of CD4+ T cell regulatory networks based on bifurcation theory by Lu, Xiaoqi, Hu, Qing, Xue, Zhuozhen, Wang, Ruiqi

“… Based on the bifurcation theory, we conduct a systematic perturbation analysis of the CD4…”
Get full text

Bifurcations and Exact Traveling Wave Solutions for the Generalized Alexeyev’s A± Equation: Bifurcations and Exact by Zhou, Yan, Zhuang, Jinsen, Li, Jibin

“… A ± equation, which we construct from the Alexeyev’s A ± equation. Based on the theory of dynamical system, we study the corresponding traveling wave system and bifurcations of its phase orbit portraits…”
Get full text

The Dynamics on Soliton Molecules and Soliton Bifurcation for an Extended Generalization of Vakhnenko Equation by Ma, Yu-Lan, Li, Bang-Qing

“… By choosing suitable parameters involved in the solutions, we identify the presence of soliton molecules and soliton bifurcation in the equation…”
Get full text

Classical and nonclassical Lie symmetries, bifurcation analysis, and Jacobi elliptic function solutions to a 3D-modified nonlinear wave equation in liquid involving gas bubbles by Alizadeh, Farzaneh, Hosseini, Kamyar, Sirisubtawee, Sekson, Hincal, Evren

“… Furthermore, the research extends into the realm of bifurcation analysis through the application of planar dynamical system theory…”
Get full text

The Exact Solutions of the Shynaray-IIA Equation Along with Analysis of Bifurcation and Chaotic Behaviors: The Exact Solutions of the Shynaray-IIA Equation by Sağlam Özkan, Yeşim

“… Thanks to the well-known bifurcation theory, phase portraits for nonlinear traveling wave solutions have been investigated…”
Get full text

Bifurcation, Phase Portrait and Traveling Wave Solutions of the Coupled Fractional Lakshmanan–Porsezian–Daniel Equation by Liu, Jing, Li, Zhao, He, Lin, Liu, Wei

“…–Daniel equation by using the dynamical system bifurcation theory approach. Based on phase portrait, we obtain some new traveling wave solutions, which include Jacobi…”
Get full text

Bifurcation and chaos in a discrete Holling–Tanner model with Beddington–DeAngelis functional response by Yang, Run, Zhao, Jianglin

“… The permanence and local stability of fixed points for the model are derived. The center manifold theorem and bifurcation theory are used to show that the model can undergo flip and Hopf bifurcations…”
Get full text

Bifurcation Analysis and Soliton Solutions to the Kuralay Equation Via Dynamic System Analysis Method and Complete Discrimination System Method by Liu, Jing, Li, Zhao

“…In this paper, the dynamical system bifurcation theory approach are employed to investigate the phase diagrams of the magnet-optic wave guides in Kuralay…”
Get full text

Bifurcation, chaos analysis and control in a discrete-time predator–prey system by Liu, Weiyi, Cai, Donghan

“…–Gower and Holling’s type II schemes is investigated on the basis of the normal form method as well as bifurcation and chaos theory…”
Get full text

Traveling Wave Solutions and Bifurcations for Generalized Fornberg–Whitham Equation with Parabolic Law Nonlinearity: Traveling Wave Solutions and Bifurcations for Generalized by Yang, Deniu

“…In this paper, the generalized Fornberg–Whitham equation with parabolic law nonlinearity is studied by the bifurcation method of differential equations and the method of phase portraits analysis…”
Get full text

Analytical Soliton Solutions to a (2 + 1)-Dimensional Variable Coefficients Graphene Sheets Equation Using the Application of Lie Symmetry Approach: Bifurcation Theory, Sensitivity Analysis and Chaotic Behavior: Analytical Soliton Solutions to a (2 + 1)-Dimensional Variable by Kumar, Sachin, Rani, Setu, Mann, Nikita

“… (vcGS) equation, which characterizes the thermophoric wave motion of wrinkles in graphene sheets…”
Get full text

Bifurcations and Exact Peakons, Periodic Peakons, Solitary Wave, Kink Wave Solutions for the Quartic CH-Type Equation: Bifurcations and Exact Peakons, Periodic Peakons, Solitary Wave by Yi, Xueqiong, Zhou, Yuqian, Liu, Qian, Li, Kebing, Zhang, Shengning

“…We introduce a novel quartic Camassa-Holm type equation and address their traveling wave solutions…”
Get full text

A Unified Analysis of Exact Traveling Wave Solutions for the Fractional-Order and Integer-Order Biswas–Milovic Equation: Via Bifurcation Theory of Dynamical System by Zhang, Bei, Zhu, Wenjing, Xia, Yonghui, Bai, Yuzhen

“… We use the conformable fractional derivatives. The method is based on the bifurcation theory of planar dynamical systems…”
Get full text

Bifurcation Analysis of a Leslie–Gower Predator–Prey Model with Allee Effect on Predator and Simplified Holling Type IV Functional Response: Bifurcation Analysis of a Leslie–Gower Predator–Prey by Zhang, Mengxin, Li, Zhong, Chen, Fengde, Chen, Lijuan

“…In this paper, a Leslie–Gower predator–prey model with simplified Holling type IV functional response and Allee effect on predator is studied…”
Get full text

Bifurcation Analysis of the Dynamics of an Unbalanced Rubber Ellipsoid of Revolution: Bifurcation Analysis of the Dynamics of an Unbalanced by Pivovarova, Elena N., Kilin, Alexander A.

“… A gyroscopic function is analyzed to examine bifurcations of partial solutions and to carry out a classification of all types of bifurcation diagrams according to parameters…”
Get full text