Browsing by Author "Idels, Lev"
Now showing items 1-17 of 17
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Bioeconomical Ricker's model of marine protected areas
(Department of Mathematics, Texas State University, 2012)Marine protected areas (MPA) become part of modern fishery management to safeguard marine life and sustain ecosystem processes. Based on a classical Ricker's model, the deterministic nonlinear sink-source model of MPA is ... -
Existence of periodic solutions in the modified Wheldon model of CML
(Department of Mathematics, Texas State University, 2013)The Wheldon model (1975) of a chronic myelogenous leukemia (CML) dynamics is modified and enriched by introduction of a time-varying microenvironment and time-dependent drug efficacies. The resulting model is a special ... -
Exponential stability of some scalar impulsive delay differential equation
(Dynamic Publishers, 1998) -
Harvesting fisheries management strategies with modified effort function [pre-print]
(Inderscience, 2008)In traditional harvesting model, a fishing effort, E, is defined by the fishing intensity and does not address the inverse effect of fish abundance on the fishing effort. In this paper, based on a canonical differential ... -
Mackey-Glass model of respiratory dynamics: Review and new results [pre-print]
(Elsevier, 2012)Since the celebrated Mackey-Glass model of respiratory dynamics was introduced in 1977, many results on its qualitative behavior have been obtained, including oscillation, stability and chaos. The paper reviews some known ... -
Mathematical model of marine protected areas [pre-print]
(Oxford University Press on behalf of the Institute of Mathematics and its Applications, 2011)We consider two regions with a fish population that is dispersing between the two areas, and fishing takes place only in region 2, with region 1 established as no-fishing zone. Marine protected areas (MPAs) have been ... -
New global exponential stability criteria for nonlinear delay differential systems with applications to BAM neural networks [pre-print]
(Elsevier, 2014-09-15)We consider a nonlinear non-autonomous system with time-varying delays (see abstract equation image) which has a large number of applications in the theory of artificial neural networks. Via the M-matrix method, easily ... -
Nicholson's blowflies differential equations revisited: Main results and open problems [post-print]
(Elsevier, 2010-06)This review covers permanence, oscillation, local and global stability of solutions for Nicholson’s blowflies differential equation. Some generalizations, including the most recent results for equations with a distributed ... -
Oscillation and asymptotic stability of a delay differential equation with Richard's nonlinearity
(Department of Mathematics, Texas State University, 2005) -
Periodic solutions of nonautonomous Mackey-type systems with delays [pre-print]
(Mathematical Research Publishers, 2013)Nonautonomous systems of delay differential equations, that model classical Mackey-type hematopoietic stem cell dynamics and Mackey-type circuit systems, are under study. Explicit sufficient and necessary conditions for ... -
[Post-print] New applications of M-matrix to stability of high-order linear delayed equations
(Elsevier, 2016-04)A substitution is introduced which exploits the parameters of the high-order delayed linear non-autonomous models and consequently allows the use of the M-matrix methods for the stability analysis. To demonstrate the ... -
Stability analysis of periodic Fox production models
(Applied Mathematics Institute, University of Alberta, 2006)In this paper we introduce a nonlinear Fox surplus production model in a periodic environment. The existence and stability of the periodic solutions of nonautonomous nonlinear differential equation (A) are analyzed. ... -
Stability of a time-varying fishing model with delay [pre-print]
(Elsevier, 2008-05)We introduce a delay differential equation model which describes how fish are harvested (see Abstract Equation Image). In our previous studies we investigated the persistence of the equation and existence of a periodic ... -
Stability of Hahnfeldt angiogenesis models with time lags [post-print]
(Elsevier, 2012-05)Mathematical models of angiogenesis, pioneered by Hahnfeldt, are under study. To enrich the dynamics of three models, we introduced biologically motivated time-varying delays. All models under study belong to a special ... -
Stability of high-order linear Itô equations with delays
(Scientific Research Publishing, 2018-03-29)A novel general stability analysis scheme based on a non-Lyapunov framework is explored. Several easy-to-check sufficient conditions for exponential p-stability are formulated in terms of M-matrices. Stability analysis ... -
Stability tests for second order linear and nonlinear delayed models [pre-print]
(Springer, 2015-02-15)For the nonlinear second order Lienard-type equations with time-varying delays (see abstract equation image) global asymptotic stability conditions are obtained. The results are based on the new sufficient stability ... -
Stabilization of second order nonlinear equations with variable delay [pre-print]
(Taylor & Francis Group, 2015)For a wide class of second-order nonlinear non-autonomous models, we illustrate that combining proportional state control with the feedback that is proportional to the derivative of the chaotic signal allows to stabilise ...
