Surface solitons supported by 𝒫𝒯-symmetric lattice with spatially modulated nonlinearity

We report on the formation and stability of induced surface solitons in parity–time ([Formula: see text]) symmetric periodic systems with spatially modulated nonlinearity. We discover that the spatially modulation of the nonlinearity can affect the existence and stability of surface solitons. These surface solitons can be formed in the semi-infinite and first bandgap. Stability analysis shows that odd surface solitons belonging to semi-infinite bandgap are linearly stably in low power domain, and the stable domain becomes narrow with increasing the strength of spatially modulated nonlinearity, both even surface solitons in semi-infinite bandgap and surface solitons in first bandgap are unstable in their existence domain.

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Defect solitons supported by nonlinear fractional Schrödinger equation with a defective lattice

Journal of Nonlinear Optical Physics & Materials ◽

10.1142/s0218863519500218 ◽

2019 ◽

Vol 28 (02) ◽

pp. 1950021

Author(s):

Yunji Meng ◽

Renxia Ning ◽

Kun Ma ◽

Zheng Jiao ◽

Haijiang Lv ◽

...

Keyword(s):

Schrödinger Equation ◽

Low Power ◽

Schrodinger Equation ◽

Fractional Schrödinger Equation ◽

Existence Domain ◽

Existence And Stability ◽

Nonlinear Fractional Schrödinger Equation ◽

Power Region ◽

Fractional Schrodinger Equation ◽

Deep Defects

We investigate numerically the existence and stability of defect solitons in nonlinear fractional Schrödinger equation. For positive defects, defect solitons are only existent in the semi-infinite gap and are stable in their whole existence domain irrespective of Lévy index. For moderate deep defects, defect solitons are existent in both the semi-infinite gap and first gap, and their instability domains occur in the low-power region of the semi-infinite gap. While for deep enough defects, stable defect solitons can be found in the second gap. Increasing the strength of defect (or Lévy index) will narrow (or broaden) the existence and stability domains.

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The Existence and Stability Analysis of Periodic Solution of Izhikevich Model

International Journal of Control Automation and Systems ◽

10.1007/s12555-019-0403-z ◽

2020 ◽

Vol 18 (5) ◽

pp. 1161-1176

Author(s):

Yi Li ◽

Chuandong Li ◽

Zhilong He ◽

Zixiang Shen

Keyword(s):

Periodic Solution ◽

Stability Analysis ◽

Existence And Stability ◽

Izhikevich Model

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Existence and Stability Analysis of Three Point Boundary Value Problem

International Journal of Applied and Computational Mathematics ◽

10.1007/s40819-017-0375-8 ◽

2017 ◽

Vol 3 (S1) ◽

pp. 651-664 ◽

Cited By ~ 10

Author(s):

Zeeshan Ali ◽

Akbar Zada ◽

Kamal Shah

Keyword(s):

Stability Analysis ◽

Boundary Value Problem ◽

Boundary Value ◽

Point Boundary ◽

Existence And Stability

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Stability Analysis of Linear Periodic Systems Via the Lyapunov Equation

IFAC Proceedings Volumes ◽

10.1016/s1474-6670(17)60971-6 ◽

1984 ◽

Vol 17 (2) ◽

pp. 213-216 ◽

Cited By ~ 6

Author(s):

S. Bittanti ◽

P. Bolzern ◽

P. Colaneri

Keyword(s):

Stability Analysis ◽

Lyapunov Equation ◽

Periodic Systems ◽

Linear Periodic Systems

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Stability Analysis of a Linear Reactor System with Feedback under Low-Flow, Low-Power Conditions

Nuclear Science and Engineering ◽

10.13182/nse93-a24493 ◽

1993 ◽

Vol 113 (3) ◽

pp. 251-263 ◽

Cited By ~ 3

Author(s):

E. V. Depiante

Keyword(s):

Stability Analysis ◽

Low Power ◽

Reactor System ◽

Low Flow

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Uplink Low-Power Scheduling for Delay-Bounded Industrial Wireless Networks Based on Imperfect Power-Domain NOMA

IEEE Systems Journal ◽

10.1109/jsyst.2019.2924483 ◽

2020 ◽

Vol 14 (2) ◽

pp. 2443-2454

Author(s):

Chaonong Xu ◽

Mianze Wu ◽

Yongjun Xu ◽

Yuguang Fang

Keyword(s):

Wireless Networks ◽

Low Power ◽

Industrial Wireless Networks ◽

Power Scheduling ◽

Power Domain

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Bifurcation and Stability Analysis of a System of Fractional-Order Differential Equations for a Plant–Herbivore Model with Allee Effect

Mathematics ◽

10.3390/math7050454 ◽

2019 ◽

Vol 7 (5) ◽

pp. 454 ◽

Cited By ~ 1

Author(s):

Ali Yousef ◽

Fatma Bozkurt Yousef

Keyword(s):

Stability Analysis ◽

Differential Equations ◽

Fractional Order ◽

Flip Bifurcation ◽

Center Manifold Theorem ◽

Fractional Order Differential Equations ◽

Existence And Stability ◽

Plant Herbivore Interaction ◽

Plant Herbivore ◽

Bifurcation And Stability

This article concerns establishing a system of fractional-order differential equations (FDEs) to model a plant–herbivore interaction. Firstly, we show that the model has non-negative solutions, and then we study the existence and stability analysis of the constructed model. To investigate the case according to a low population density of the plant population, we incorporate the Allee function into the model. Considering the center manifold theorem and bifurcation theory, we show that the model shows flip bifurcation. Finally, the simulation results agree with the theoretical studies.

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