v. kocic | Xavier University of Louisiana (original) (raw)
Papers by v. kocic
Applicable Analysis and Discrete Mathematics, 2015
Our aim is to investigate the global asymptotic behavior, the existence of invariant intervals, o... more Our aim is to investigate the global asymptotic behavior, the existence of invariant intervals, oscillatory behavior, structure of semicycles, and periodicity of a nonlinear discrete population model of the form xn+1= F(xn); for n = 0,1,...,where x0> 0; and the function F is a positive piecewise continuous function with two jump discontinuities satisfying some additional conditions. The motivation for study of this general model was inspired by the classical Williamson's discontinuous population model, some recent results about the dynamics of the discontinuous Beverton-Holt model, and applications of discontinuous maps to the West Nile epidemic model. In the first section we introduce the population model which is a focal point of this paper. We provide background information including a summary of related results, a comparison between characteristics of continuous and discontinuous population models (with and without the Allee-type effect), and a justification of hypotheses...
Journal of Mathematical Analysis and Applications, 1993
Journal of Difference Equations and Applications, 2010
It is well known that the periodic cycle of a periodically forced non-linear difference equation ... more It is well known that the periodic cycle of a periodically forced non-linear difference equation is attenuant (resonant) if , where {K n } is the carrying capacity of the environment and (arithmetic mean of the p-periodic cycle {t n }). In this paper, we introduce the concept of g-attenuance and g-resonance of periodic cycles by using the geometric mean for the average of a periodic cycle instead of the arithmetic mean. For the general class of periodically forced population models with delay
Journal of Difference Equations and Applications, 2005
... xnþ1 ¼ rKnxn Kn þ ðr 2 1Þxn , n ¼ 0, 1, .... ð2Þ Cushing and Henson [2] formulated the follow... more ... xnþ1 ¼ rKnxn Kn þ ðr 2 1Þxn , n ¼ 0, 1, .... ð2Þ Cushing and Henson [2] formulated the following conjecture for equation (2): ... Corresponding author. E-mail: vkocic@xula.edu Journal of Difference Equations and Applications, Vol. 11, No. 45, April 2005, 415422 ...
Journal of Biological Dynamics, 2010
It is well known that the periodic cycle {x(n)} of a periodically forced nonlinear difference equ... more It is well known that the periodic cycle {x(n)} of a periodically forced nonlinear difference equation is attenuant (resonant) if av(x(n)) < av(K(n))(av(x(n)) > av(K(n))),where {K ( n )} is the carrying capacity of the environment and av(t(n)) = (1/p)∑(p−1) (i=0) ti (arithmetic mean of the p-periodic cycle {t ( n )}). In this article, we extend the concept of attenuance and resonance of periodic cycles using the geometric mean for the average of a periodic cycle. We study the properties of the periodically forced nonautonomous delay Beverton-Holt model x(n+1) = r(n)x(n)/1 + (r(n−l) − 1)x(n−k)/K(n−k), n= 0, 1, . . . , where {K ( n )} and {r ( n )} are positive p-periodic sequences; (K ( n )>0, r ( n )>1) as well as k and l are nonnegative integers. We will show that for all positive solutions {x ( n )} of the previous equation lim sup (n→∞) (∏(n−1)(i=0)xi)(1/n) ≤ ((∏(p−1)(i=0)ri)(1/p) − 1)(∏(p−1)(i=0)(ri − 1))(−1/p)(∏(p−1)(i=0)Ki)(1/p). In particular, in the case where {x(n)} is a p-periodic solution of the above equation (assuming that such solution exists) and r ( n )=r>1, the periodic cycle is g-attenuant, that is (∏(p−1)(i=0)x(i))(1/p)<(∏(p−1)(i=0)K(i))(p−1) Surprisingly, the obtained results show that the delays k and l do not play any role.
Journal of Mathematical Analysis and Applications, 2000
Journal of Difference Equations and Applications, 1997
... 4MS Subject Ckuss~jic~uri~n. 39A 10 1 INTRODUCTION AND PRELIMINARIES Consider the difference ... more ... 4MS Subject Ckuss~jic~uri~n. 39A 10 1 INTRODUCTION AND PRELIMINARIES Consider the difference equation *Corresponding author. Tel.: 504-485-5309 exL. 6717. Fax: 504-485-7928. E-mail: vkocicio mail.xula.edu. Page 2. where ...
Journal of Mathematical Analysis and Applications, 1993
Communications on Pure and Applied Mathematics, 1995
In this paper we obtain a global attractivity result for the positive equilibrium of a nonlinear ... more In this paper we obtain a global attractivity result for the positive equilibrium of a nonlinear second-order difference equation of the form xn+1 = f(xn, xn+1), n = 0, 1, ⃛The result applies to the difference equation xn+1 =A+bxn/A+n−1, n = 0, 1, ⃛Where a, b, A ϵ (0, ∞). © 1996 John Wiley & Sons, Inc.
Proceedings of The American Mathematical Society, 1992
We obtain a set of sufficient conditions under which all positive solutions of the nonlinear dela... more We obtain a set of sufficient conditions under which all positive solutions of the nonlinear delay difference equation x"+l = x"f(xn_k), n = 0,1,2,..., are attracted to the positive equilibrium of the equation. Our result applies, for example, to the delay logistic model JVI+i = aN¡/(\ +ßNt_k) and to the delay difference equation xn+i = x"er^~x"-k'1 .
Mathematics and Its Applications VL Kocic and G. Ladas Global Behavior of Nonlinear Difference Eq... more Mathematics and Its Applications VL Kocic and G. Ladas Global Behavior of Nonlinear Difference Equations of Higher Order with Applications Kluwer Academic Publishers Page 2. ... Global Behavior of Nonlinear Difference Equations of Higher Order with Applications Page 8. ...
Hiroshima Mathematical Journal, 1992
Journal of Difference Equations and Applications, 1996
Journal of Difference Equations and Applications, 2004
... VL KOCIC, D. STUTSON and G. ARORA Department of Mathematics, Xavier University of Louisiana, ... more ... VL KOCIC, D. STUTSON and G. ARORA Department of Mathematics, Xavier University of Louisiana, New Orleans, LA 70125, USA ... Assume, for the sake of contradiction that x . 0. Let {ni} be a sequence of positive integers such that limi!1 ani ¼ lim supn!1 an ¼ b. Then ...
Applicable Analysis, 1990
ABSTRACT
Journal of Difference Equations and Applications, 2005
... We study the global asymptotic behavior of solutions of the nonautonomous difference equation... more ... We study the global asymptotic behavior of solutions of the nonautonomous difference equation. where {p n } is a positive bounded sequence and the initial conditions are positive. ... In addition, we obtain global attractivity results. The results are applied to the case when {p n } is ...
Journal of Difference Equations and Applications, 1995
Journal of Difference Equations and Applications, 1997
... 4MS Subject Ckuss~jic~uri~n. 39A 10 1 INTRODUCTION AND PRELIMINARIES Consider the difference ... more ... 4MS Subject Ckuss~jic~uri~n. 39A 10 1 INTRODUCTION AND PRELIMINARIES Consider the difference equation *Corresponding author. Tel.: 504-485-5309 exL. 6717. Fax: 504-485-7928. E-mail: vkocicio mail.xula.edu. Page 2. where ...
Proceedings of The American Mathematical Society, 1992
We obtain a set of sufficient conditions under which all positive solutions of the nonlinear dela... more We obtain a set of sufficient conditions under which all positive solutions of the nonlinear delay difference equation x"+l = x"f(xn_k), n = 0,1,2,..., are attracted to the positive equilibrium of the equation. Our result applies, for example, to the delay logistic model JVI+i = aN¡/(\ +ßNt_k) and to the delay difference equation xn+i = x"er^~x"-k'1 .
Applicable Analysis and Discrete Mathematics, 2015
Our aim is to investigate the global asymptotic behavior, the existence of invariant intervals, o... more Our aim is to investigate the global asymptotic behavior, the existence of invariant intervals, oscillatory behavior, structure of semicycles, and periodicity of a nonlinear discrete population model of the form xn+1= F(xn); for n = 0,1,...,where x0> 0; and the function F is a positive piecewise continuous function with two jump discontinuities satisfying some additional conditions. The motivation for study of this general model was inspired by the classical Williamson's discontinuous population model, some recent results about the dynamics of the discontinuous Beverton-Holt model, and applications of discontinuous maps to the West Nile epidemic model. In the first section we introduce the population model which is a focal point of this paper. We provide background information including a summary of related results, a comparison between characteristics of continuous and discontinuous population models (with and without the Allee-type effect), and a justification of hypotheses...
Journal of Mathematical Analysis and Applications, 1993
Journal of Difference Equations and Applications, 2010
It is well known that the periodic cycle of a periodically forced non-linear difference equation ... more It is well known that the periodic cycle of a periodically forced non-linear difference equation is attenuant (resonant) if , where {K n } is the carrying capacity of the environment and (arithmetic mean of the p-periodic cycle {t n }). In this paper, we introduce the concept of g-attenuance and g-resonance of periodic cycles by using the geometric mean for the average of a periodic cycle instead of the arithmetic mean. For the general class of periodically forced population models with delay
Journal of Difference Equations and Applications, 2005
... xnþ1 ¼ rKnxn Kn þ ðr 2 1Þxn , n ¼ 0, 1, .... ð2Þ Cushing and Henson [2] formulated the follow... more ... xnþ1 ¼ rKnxn Kn þ ðr 2 1Þxn , n ¼ 0, 1, .... ð2Þ Cushing and Henson [2] formulated the following conjecture for equation (2): ... Corresponding author. E-mail: vkocic@xula.edu Journal of Difference Equations and Applications, Vol. 11, No. 45, April 2005, 415422 ...
Journal of Biological Dynamics, 2010
It is well known that the periodic cycle {x(n)} of a periodically forced nonlinear difference equ... more It is well known that the periodic cycle {x(n)} of a periodically forced nonlinear difference equation is attenuant (resonant) if av(x(n)) < av(K(n))(av(x(n)) > av(K(n))),where {K ( n )} is the carrying capacity of the environment and av(t(n)) = (1/p)∑(p−1) (i=0) ti (arithmetic mean of the p-periodic cycle {t ( n )}). In this article, we extend the concept of attenuance and resonance of periodic cycles using the geometric mean for the average of a periodic cycle. We study the properties of the periodically forced nonautonomous delay Beverton-Holt model x(n+1) = r(n)x(n)/1 + (r(n−l) − 1)x(n−k)/K(n−k), n= 0, 1, . . . , where {K ( n )} and {r ( n )} are positive p-periodic sequences; (K ( n )>0, r ( n )>1) as well as k and l are nonnegative integers. We will show that for all positive solutions {x ( n )} of the previous equation lim sup (n→∞) (∏(n−1)(i=0)xi)(1/n) ≤ ((∏(p−1)(i=0)ri)(1/p) − 1)(∏(p−1)(i=0)(ri − 1))(−1/p)(∏(p−1)(i=0)Ki)(1/p). In particular, in the case where {x(n)} is a p-periodic solution of the above equation (assuming that such solution exists) and r ( n )=r>1, the periodic cycle is g-attenuant, that is (∏(p−1)(i=0)x(i))(1/p)<(∏(p−1)(i=0)K(i))(p−1) Surprisingly, the obtained results show that the delays k and l do not play any role.
Journal of Mathematical Analysis and Applications, 2000
Journal of Difference Equations and Applications, 1997
... 4MS Subject Ckuss~jic~uri~n. 39A 10 1 INTRODUCTION AND PRELIMINARIES Consider the difference ... more ... 4MS Subject Ckuss~jic~uri~n. 39A 10 1 INTRODUCTION AND PRELIMINARIES Consider the difference equation *Corresponding author. Tel.: 504-485-5309 exL. 6717. Fax: 504-485-7928. E-mail: vkocicio mail.xula.edu. Page 2. where ...
Journal of Mathematical Analysis and Applications, 1993
Communications on Pure and Applied Mathematics, 1995
In this paper we obtain a global attractivity result for the positive equilibrium of a nonlinear ... more In this paper we obtain a global attractivity result for the positive equilibrium of a nonlinear second-order difference equation of the form xn+1 = f(xn, xn+1), n = 0, 1, ⃛The result applies to the difference equation xn+1 =A+bxn/A+n−1, n = 0, 1, ⃛Where a, b, A ϵ (0, ∞). © 1996 John Wiley & Sons, Inc.
Proceedings of The American Mathematical Society, 1992
We obtain a set of sufficient conditions under which all positive solutions of the nonlinear dela... more We obtain a set of sufficient conditions under which all positive solutions of the nonlinear delay difference equation x"+l = x"f(xn_k), n = 0,1,2,..., are attracted to the positive equilibrium of the equation. Our result applies, for example, to the delay logistic model JVI+i = aN¡/(\ +ßNt_k) and to the delay difference equation xn+i = x"er^~x"-k'1 .
Mathematics and Its Applications VL Kocic and G. Ladas Global Behavior of Nonlinear Difference Eq... more Mathematics and Its Applications VL Kocic and G. Ladas Global Behavior of Nonlinear Difference Equations of Higher Order with Applications Kluwer Academic Publishers Page 2. ... Global Behavior of Nonlinear Difference Equations of Higher Order with Applications Page 8. ...
Hiroshima Mathematical Journal, 1992
Journal of Difference Equations and Applications, 1996
Journal of Difference Equations and Applications, 2004
... VL KOCIC, D. STUTSON and G. ARORA Department of Mathematics, Xavier University of Louisiana, ... more ... VL KOCIC, D. STUTSON and G. ARORA Department of Mathematics, Xavier University of Louisiana, New Orleans, LA 70125, USA ... Assume, for the sake of contradiction that x . 0. Let {ni} be a sequence of positive integers such that limi!1 ani ¼ lim supn!1 an ¼ b. Then ...
Applicable Analysis, 1990
ABSTRACT
Journal of Difference Equations and Applications, 2005
... We study the global asymptotic behavior of solutions of the nonautonomous difference equation... more ... We study the global asymptotic behavior of solutions of the nonautonomous difference equation. where {p n } is a positive bounded sequence and the initial conditions are positive. ... In addition, we obtain global attractivity results. The results are applied to the case when {p n } is ...
Journal of Difference Equations and Applications, 1995
Journal of Difference Equations and Applications, 1997
... 4MS Subject Ckuss~jic~uri~n. 39A 10 1 INTRODUCTION AND PRELIMINARIES Consider the difference ... more ... 4MS Subject Ckuss~jic~uri~n. 39A 10 1 INTRODUCTION AND PRELIMINARIES Consider the difference equation *Corresponding author. Tel.: 504-485-5309 exL. 6717. Fax: 504-485-7928. E-mail: vkocicio mail.xula.edu. Page 2. where ...
Proceedings of The American Mathematical Society, 1992
We obtain a set of sufficient conditions under which all positive solutions of the nonlinear dela... more We obtain a set of sufficient conditions under which all positive solutions of the nonlinear delay difference equation x"+l = x"f(xn_k), n = 0,1,2,..., are attracted to the positive equilibrium of the equation. Our result applies, for example, to the delay logistic model JVI+i = aN¡/(\ +ßNt_k) and to the delay difference equation xn+i = x"er^~x"-k'1 .