Browsing by Author "Idels, Lev"
Now showing items 1-18 of 18
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Bioeconomical Ricker's model of marine protected areas
(Department of Mathematics, Texas State University, 2012-05-14)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, 2013-12-17)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)Explicit exponential stability results are obtained for a scalar delay differential equation (see abstract image). -
Oscillation and asymptotic stability of a delay differential equation with Richard's nonlinearity
(Department of Mathematics, Texas State University, 2005-04-20)We obtain sufficient conditions for oscillation of solutions, and for asymptotical stability of the positive equilibrium, of a scalar nonlinear delay differential equation (see abstract image). -
[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 ... -
[Post-print] Nicholson's blowflies differential equations revisited: Main results and open problems
(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 ... -
[Post-print] Stability of Hahnfeldt angiogenesis models with time lags
(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 ... -
[Pre-print] Harvesting fisheries management strategies with modified effort function
(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 ... -
[Pre-print] Mackey-Glass model of respiratory dynamics: Review and new results
(Elsevier, 2012-11)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 ... -
[Pre-print] Mathematical model of marine protected areas
(Oxford University Press on behalf of the Institute of Mathematics and its Applications, 2011-04)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 ... -
[Pre-print] New global exponential stability criteria for nonlinear delay differential systems with applications to BAM neural networks
(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 ... -
[Pre-print] Periodic solutions of nonautonomous Mackey-type systems with delays
(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 ... -
[Pre-print] Stability of a time-varying fishing model with delay
(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 ... -
[Pre-print] Stability tests for second order linear and nonlinear delayed models
(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 ... -
[Pre-print] Stabilization of second order nonlinear equations with variable delay
(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 ... -
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 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 ... -
Stochastic McKendrick-Von Foerster models with applications
(Elsevier, 2020-01-01)A newly presented McKendrick–Von Foerster model with a stochastically perturbed mortality rate is examined. A transformation method converting the model with nonlocal boundary conditions into a system of stochastic ...
