Invariant algebraic surfaces for the reduced three-wave interaction system

A one-parameter family of differential systems that bridges the gap between the Lorenz and the Chen systems was proposed by Lu, Chen, Cheng and Celikovsy. The goal of this paper is to analyze what we can say using analytic tools about the dynamics of this one-parameter family of differential systems. We shall describe its global dynamics at infinity, and for two special values of the parameter a we can also describe the global dynamics in the whole ℝ3using the invariant algebraic surfaces of the family. Additionally we characterize the Hopf bifurcations of this family.

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N -soliton solutions for the nonlocal two-wave interaction system via the Riemann–Hilbert method

Chinese Physics B ◽

10.1088/1674-1056/27/12/120202 ◽

2018 ◽

Vol 27 (12) ◽

pp. 120202 ◽

Cited By ~ 1

Author(s):

Si-Qi Xu ◽

Xian-Guo Geng

Keyword(s):

Soliton Solutions ◽

Wave Interaction ◽

Interaction System

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Dynamical Analysis on a Finance System with Nonconstant Elasticity of Demand

International Journal of Bifurcation and Chaos ◽

10.1142/s0218127420501485 ◽

2020 ◽

Vol 30 (10) ◽

pp. 2050148

Author(s):

Ting Yang

Keyword(s):

Chaotic Attractor ◽

Period Doubling ◽

Approximate Expression ◽

Algebraic Surfaces ◽

Dynamical Analysis ◽

Periodic Attractor ◽

Normal Form Theory ◽

Finance System ◽

Elasticity Of Demand ◽

Invariant Algebraic Surfaces

This paper investigates a finance system with nonconstant elasticity of demand. First, under some conditions, the system has invariant algebraic surfaces and the analytic expressions of the surfaces are given. Furthermore, when the two surfaces coincide and become one surface, the dynamics on the surface are analyzed and a globally stable equilibrium is found. Second, by using the normal form theory, the Hopf bifurcation is studied and the approximate expression and stability of the bifurcating periodic orbit are obtained. Third, the chaotic behaviors are investigated and the route to chaos is period-doubling bifurcations. Moreover, it is found that the system has coexisting attractors, including periodic attractor and periodic attractor, chaotic attractor and chaotic attractor. With the change of parameter, the two chaotic attractors coincide and then a symmetrical chaotic attractor arises.

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On the exact solitary wave solutions to the long-short wave interaction system

ITM Web of Conferences ◽

10.1051/itmconf/20182201063 ◽

2018 ◽

Vol 22 ◽

pp. 01063

Author(s):

Haci Mehmet Baskonus ◽

Tukur Abdulkadir Sulaiman ◽

Hasan Bulut

Keyword(s):

Solitary Wave ◽

Wave Interaction ◽

Expansion Method ◽

Short Wave ◽

Complex Model ◽

Solitary Wave Solutions ◽

Short Transverse ◽

Wave Solutions ◽

Interaction System ◽

2D And 3D

In this paper, the application of the simplified the extended sinh-Gordon equation expansion method to the long-short-wave interaction system. We successfully construct various solitary wave solutions to this nonlinear complex model. The long-short-wave interaction system describes the interaction between one long longitudinal wave and one short transverse wave propagating in a generalized elastic medium. The 2D and 3D surfaces to some of the obtained solutions are plotted.

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