Stability of Planar Nonlinear Switched Systems [PDF]
arXiv, 2005 We consider the time-dependent nonlinear system $\dot q(t)=u(t)X(q(t))+(1-u(t))Y(q(t))$, where $q\in\R^2$, $X$ and $Y$ are two %$C^\infty$ smooth vector fields, globally asymptotically stable at the origin and $u:[0,\infty)\to\{0,1\}$ is an arbitrary measurable function.
arxiv
A global convergence result for strongly monotone systems with positive translation invariance [PDF]
arXiv, 2006 We show that strongly monotone systems of ordinary differential equations which have a certain translation-invariance property are so that all solutions converge to a unique equilibrium. The result may be seen as a dual of a well-known theorem of Mierczynski for systems that satisfy a conservation law.
arxiv
Global stability of latency-age/stage-structured epidemic models with differential infectivity. [PDF]
J Math Biol, 2023 Liu X, Chen Y, Li X, Li J.
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A variational proof of global stability for bistable travelling waves [PDF]
arXiv, 2006 We give a variational proof of global stability for bistable travelling waves of scalar reaction-diffusion equations on the real line. In particular, we recover some of the classical results by P. Fife and J.B. McLeod without any use of the maximum principle.
arxiv
H ∞ state estimation of quaternion-valued inertial neural networks: non-reduced order method. [PDF]
Cogn Neurodyn, 2023 Tu Z +6 more
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Analele Stiintifice ale Universitatii Ovidius Constanta: Seria MatematicaIn this article, we study the existence of mild solutions of a non-instantaneous integrodi erential equations on unbounded domain via resolvent operators in Banach space. For our proofs, we employ the semigroups theory and Schauder’s fixed point theorem.
Bensalem Abdelhamid +3 more
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Contraction in $L^1$ and large time behavior for a system arising in chemical reactions and molecular motors [PDF]
arXiv, 2008 We prove a contraction in $L^1$ property for the solutions of a nonlinear reaction--diffusion system whose special cases include intercellular transport as well as reversible chemical reactions. Assuming the existence of stationary solutions we show that the solutions stabilize as $t$ tends to infinity.
arxiv
Optimal control and cost-effectiveness analysis of a new COVID-19 model for Omicron strain. [PDF]
Physica A, 2022 Li T, Guo Y.
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An observation regarding systems which converge to steady states for all constant inputs, yet become chaotic with periodic inputs [PDF]
arXiv, 2009 This note provides a general construction, and gives a concrete example of, forced ordinary differential equation systems that have these two properties: (a) for each constant input u, all solutions converge to a steady state but (b) for some periodic inputs, the system has arbitrary (for example, "chaotic") behavior.
arxiv
Global Stability of a Mumps Transmission Model with Quarantine Measure. [PDF]
Acta Math Appl Sin, 2021 Bai YZ, Wang XJ, Guo SB.
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