American Institute of Mathematical Sciences

Advanced
2011, 2011(Special): 1042-1051. doi: 10.3934/proc.2011.2011.1042

Positivity, robust stability and comparison of dynamic systems

Alexey G. Mazko 1,

1. 

Institute of Mathematics, National Academy of Sciences of Ukraine, Tereshchenkivs'ka Str., 3, Kyiv, 01601, Ukraine

Received  June 2010 Revised  April 2011 Published  October 2011

We study generalized classes of positive and monotone dynamic systems in a partially ordered Banach space. Using results from the nonlinear operators theory, we establish new algebraic conditions for stability of equilibrium states of a class of monotone-type di fferential and diff erence systems. Conditions for the positivity and absolute stability of diff erential systems with delay are proposed. Using new technique for constructing the invariant sets of diff erential systems, we generalize known positivity conditions for linear and nonlinear diff erential systems with respect to typical classes of cones. In addition, we generalize the comparison principle for a finite set of diff erential systems and formulate robust stability conditions for some families of diff erential systems in terms of cone inequalities.
Keywords: Positive system, Cone, Lyapunov stability, Monotone system.
Mathematics Subject Classification: Primary: 34D20, 47H07; Secondary: 34C12, 47A50.
Citation: Alexey G. Mazko. Positivity, robust stability and comparison of dynamic systems. Conference Publications, 2011, 2011 (Special) : 1042-1051. doi: 10.3934/proc.2011.2011.1042
[1]

Yuxia Guo, Jianjun Nie. Classification for positive solutions of degenerate elliptic system. Discrete & Continuous Dynamical Systems - A, 2019, 39 (3) : 1457-1475. doi: 10.3934/dcds.2018130
[2]

Diane Denny. A unique positive solution to a system of semilinear elliptic equations. Conference Publications, 2013, 2013 (special) : 193-195. doi: 10.3934/proc.2013.2013.193
[3]

Jing Liu, Xiaodong Liu, Sining Zheng, Yanping Lin. Positive steady state of a food chain system with diffusion. Conference Publications, 2007, 2007 (Special) : 667-676. doi: 10.3934/proc.2007.2007.667
[4]

Xiangnan He, Wenlian Lu, Tianping Chen. On transverse stability of random dynamical system. Discrete & Continuous Dynamical Systems - A, 2013, 33 (2) : 701-721. doi: 10.3934/dcds.2013.33.701
[5]

Claudia Valls. Stability of some waves in the Boussinesq system. Communications on Pure & Applied Analysis, 2006, 5 (4) : 929-939. doi: 10.3934/cpaa.2006.5.929
[6]

Gunther Dirr, Hiroshi Ito, Anders Rantzer, Björn S. Rüffer. Separable Lyapunov functions for monotone systems: Constructions and limitations. Discrete & Continuous Dynamical Systems - B, 2015, 20 (8) : 2497-2526. doi: 10.3934/dcdsb.2015.20.2497
[7]

Jiawei Dou, Lan-sun Chen, Kaitai Li. A monotone-iterative method for finding periodic solutions of an impulsive competition system on tumor-normal cell interaction. Discrete & Continuous Dynamical Systems - B, 2004, 4 (3) : 555-562. doi: 10.3934/dcdsb.2004.4.555
[8]

Joachim Naumann. On the existence of weak solutions of an unsteady p-Laplace thermistor system with strictly monotone electrical conductivities. Discrete & Continuous Dynamical Systems - S, 2017, 10 (4) : 837-852. doi: 10.3934/dcdss.2017042
[9]

Jeongsim Kim, Bara Kim. Stability of a cyclic polling system with an adaptive mechanism. Journal of Industrial & Management Optimization, 2015, 11 (3) : 763-777. doi: 10.3934/jimo.2015.11.763
[10]

Xiaojie Hou, Wei Feng. Traveling waves and their stability in a coupled reaction diffusion system. Communications on Pure & Applied Analysis, 2011, 10 (1) : 141-160. doi: 10.3934/cpaa.2011.10.141
[11]

Hichem Kasri, Amar Heminna. Exponential stability of a coupled system with Wentzell conditions. Evolution Equations & Control Theory, 2016, 5 (2) : 235-250. doi: 10.3934/eect.2016003
[12]

Takayoshi Ogawa, Hiroshi Wakui. Stability and instability of solutions to the drift-diffusion system. Evolution Equations & Control Theory, 2017, 6 (4) : 587-597. doi: 10.3934/eect.2017029
[13]

Jacques Féjoz. On "Arnold's theorem" on the stability of the solar system. Discrete & Continuous Dynamical Systems - A, 2013, 33 (8) : 3555-3565. doi: 10.3934/dcds.2013.33.3555
[14]

Shubo Zhao, Ping Liu, Mingchao Jiang. Stability and bifurcation analysis in a chemotaxis bistable growth system. Discrete & Continuous Dynamical Systems - S, 2017, 10 (5) : 1165-1174. doi: 10.3934/dcdss.2017063
[15]

István Györi, Ferenc Hartung. Exponential stability of a state-dependent delay system. Discrete & Continuous Dynamical Systems - A, 2007, 18 (4) : 773-791. doi: 10.3934/dcds.2007.18.773
[16]

Jingli Ren, Zhibo Cheng, Stefan Siegmund. Positive periodic solution for Brillouin electron beam focusing system. Discrete & Continuous Dynamical Systems - B, 2011, 16 (1) : 385-392. doi: 10.3934/dcdsb.2011.16.385
[17]

Yayun Li, Yutian Lei. On existence and nonexistence of positive solutions of an elliptic system with coupled terms. Communications on Pure & Applied Analysis, 2018, 17 (5) : 1749-1764. doi: 10.3934/cpaa.2018083
[18]

Shiren Zhu, Xiaoli Chen, Jianfu Yang. Regularity, symmetry and uniqueness of positive solutions to a nonlinear elliptic system. Communications on Pure & Applied Analysis, 2013, 12 (6) : 2685-2696. doi: 10.3934/cpaa.2013.12.2685
[19]

Zhanping Liang, Yuanmin Song, Fuyi Li. Positive ground state solutions of a quadratically coupled schrödinger system. Communications on Pure & Applied Analysis, 2017, 16 (3) : 999-1012. doi: 10.3934/cpaa.2017048
[20]

Haidong Liu, Zhaoli Liu. Positive solutions of a nonlinear Schrödinger system with nonconstant potentials. Discrete & Continuous Dynamical Systems - A, 2016, 36 (3) : 1431-1464. doi: 10.3934/dcds.2016.36.1431

 Impact Factor: 

Tools

Metrics

  • PDF downloads (13)
  • HTML views (0)
  • Cited by (0)

Other articles
by authors

[Back to Top]

Copyright © 2020 American Institute of Mathematical Sciences