differential equations
6.2 Publications and conference lectures
6.2.3 International conference presentations related to the ThesisThesis
(C1) Istv´an Gy˝ori, Ferenc Hartung, Nahed A. Mohamady, Boundedness of so-lutions of nonlinear delay differential equations, 10th Colloquium on the Qual-itative Theory of Differential Equations 2015, Bolyai Institute, University of Szeged, Hungary, July 1-4, 2015.
(C2) Istv´an Gy˝ori, Ferenc Hartung,Nahed A. Mohamady,Persistence and Per-manence of Nonlinear Delay Population Models, The Second International Conference on New Horizons in Basic and Applied Science, Hurghada , Egypt, August 1-6, 2015.
(C3) Istv´an Gy˝ori, Ferenc Hartung, Nahed A. Mohamady, Boundedness of positive solutions of a system of nonlinear delay differential equations, O.D.
EQUATIONS BRNO 2016, Faculty of Science, Masaryk University, Brno, Czech Republic, June 6 - 8, 2016.
[1] M. Akhmet, Nonlinear Hybrid Continuous/Discrete-Time Models, Atlantis Press, Amsterdam Paris, 2011.
[2] J. Arino, L. Wang, G.S. Wolkowicz, An alternative formulation for a delayed logistic equation, J. Theor. Biol. 241 (1) (2006) 109–119.
[3] J. Baˇstinec, L. Berezansky, J. Diblik, Z. ˇSmarda, On a delay population model with quadratic nonlinearity, Adv. Difference Equ. 2012 (2012) 230.
[4] J. Baˇstinec, L. Berezansky, J. Diblik, Z. ˇSmarda, On a delay population model with a quadratic nonlinearity without positive steady state, Appl. Math. Com-put. 227 (2014) 622–629.
[5] A. Bellen, M. Zennaro, Numerical Methods for Delay Differential Equations, Oxford University Press, 2003.
[6] L. Berezansky, E. Braverman, L. Idels, Nicholson’s blowflies differential equa-tions revisited: main results and open problems, Appl. Math. Model. 34 (2010) 1405–1417.
[7] L. Berezansky, L. Idels and L. Troib, Global dynamics of Nicholson-type delay systems with applications, Nonlinear Anal. Real World Appl., 12, (2011) 436–
445.
[8] L. Berezansky, E. Braverman, On stability of cooperative and hereditary sys-tems with a distributed delay, Nonlinearity 28:6 (2015) 1745–1760.
95
[9] L. Berezansky, E. Braverman, Boundedness and persistence of delay differential equations with mixed nonlinearity, Appl. Math. Comput. 279 (2016) 154–169.
[10] A. Berman, R.J. Plemmons, Nonnegative Matrices in the Mathematical Sci-ences, (Academic Press, New York, 1979)
[11] G.I. Bischi, Compartmental analysis of economic systems with heterogeneous agents: an introduction, in Beyond the Representative Agent, ed. A. Kirman, M. Gallegati (Elgar Pub. Co., 1998) pp. 181–214
[12] S. P. Blythe, R. M. Nisbet and W. S. C. Gurney, Instability and complex dynamic behaviour in population models with long time delays, Theor. Pop.
Biol. 22 (1982) 147–176.
[13] G. Bonanno, P. Candito, G. D’Agui, Positive solutions for a nonlinear parameter-depending algebraic system, Electron. J. Diff. Equ., (2015)(17) 1–14 (2015)
[14] R.F. Brown, Compartmental system analysis: state of the art. IEEE Trans.
Biomed. Eng., BME-27:1 (1980) 1–11.
[15] M. Budincevic, A comparison theorem of differential equations, Novi Sad J.
Math., 40(1), (2010) 55–56.
[16] A. Chen, L. Huang, J. Cao, Existence and stability of almost periodic solution for BAM neural networks with delays, Appl. Math. Comput., 137 (2003) 177–
193.
[17] S. Chen, Q. Zhang, C. Wang, Existence and stability of eqilibria of the continuous-time Hopfield neural network. J. Comp. Appl. Math., 169 (2004) 117–125.
[18] C.Y. Cheng, K.H. Lin, C.W. Shih, Multistability and convergence in delayed neural networks. Phys. D, 225(2007) 61–74.
[19] L.O. Chua, L. Yang, Cellular neural networks: Theory. IEEE Trans. Circuits Syst., 35 (1988) 1257–1272.
[20] A. Ciurte, S. Nedevschi, I. Rasa : An algorithm for solving some nonlinear sys-tems with applications to extremum problems, Taiwan. J. Math., 16(3)(2012) 1137-1150.
[21] A. Ciurte, S. Nedevschi, I. Rasa: Systems of nonlinear algebraic equations with unique solution, Numer Algor., 68 (2015) 367-376.
[22] K.L. Cooke and J. Wiener, Retarded differential equations with piecewise con-stant delays, J. Math. Anal. Appl., 99 (1984), 265–297.
[23] K.L. Cooke and J. Wiener, Stability regions for linear equations with piecewise continuous delays, Comput. Math. Appl., 12A (1986) 695–701.
[24] K.L. Cooke and J. Wiener, A survey of differential equations with piecewise continuous arguments, Delay Differential Equations and Dynamical Systems, eds. S. Busenberg and M. Martelli (Lecture Notes in Math. 1475), Springer-Verlag, Berlin (1991), 1–15.
[25] K. Cooke, P. van den Driessche and X. Zou, Interaction of maturation delay and nonlinear birth in population and epidemic models, J. Math. Biol., 39 (1999) 332–352.
[26] J. M. Cushing, Integrodifferential Equations and Delay Models in Population Dynamics, Lecture Notes in Biomathematics 20, Springer-Verlag, Heidelberg (1977).
[27] J. M. Cushing, Time delays in single growth models, J. Math. Biol., 4 (1977)257–264.
[28] P. Das, A. B. Roy, A. Das, Stability and oscilations of a negative feedback delay model for the control of testosterone secretion, BioSystems, 32 (1994) 61–69.
[29] P. van den Driessche and X. Zou, Global attractivity in delayed Hopfield neural network models, SIAM J. on Appl. Math., 58:6 (1998) 1878–1890.
[30] R.D. Driver, Ordinary and Delay Differential Equations, (Berlin:Springer, 1977) [31] T. Faria, A note on permanence of nonautonomous cooperative scalar
popula-tion models with delays, Appl. Math. Comput., 240 (2014) 82–90.
[32] T. Faria, Persistence and permanence for a class of functional differential equa-tions with infinite delay, J. Dyn. Diff. Equat., 28(3) (2016) 1163–1186.
[33] T. Faria, G. R¨ost, Persistence, permanence and global stability for an n-dimensional Nicholson system, J. Dyn. Diff. Equat., 26 (2014) 723–744.
[34] L. Farina, S. Rinaldi, Positive Linear Systems, Theory and Application (Wiley-lnterscience, 2000)
[35] K. Gopalsamy, Stability and Oscillations in Delay Differential Equations of Population Dynamics, Mathematics and its Applications, vol. 74, Kluwer Aca-demic Publishers Group, Dordrecht, 1992.
[36] K. Gopalsamy, X. He, Stability in asymmetric Hopfield nets with transmission delays, Phys. D., 76 (1994) 344–358.
[37] W. S. C. Gurney, S. P. Blythe , and R. M. Nisbet. Nicholson’s blowflies revisited, Nature 287, (1980)17-–21.
[38] I. Gy˝ori, Asymptotic stability and oscillations of linear non-autonomous delay differential equations, In: Proceedings of International Conference in Colombus, Ohio, March 21-25, 1989, University Press, Athens, 1989, pp. 389–397.
[39] I. Gy˝ori, Connections between compartmental systems with pipes and integro-differential equations. Math. Model., 7(9-12)(1986) 1215–1238.
[40] I. Gy˝ori, Approximation of the solution of delay differential equations by using piecewise constant arguments, Internat. J. Math. Math. Sci. 14 (1991), 111–126.
[41] I. Gy˝ori, J. Eller, Compartmental systems with pipes, Math. Biosci., 53(3) (1981) 223–247.
[42] I. Gy˝ori and F. Hartung, Stability in delay perturbed differential and difference equations, Fields Inst. Commu., 29 (2001) 181–194.
[43] I. Gy˝ori and F. Hartung, On numerical approximation using differential equa-tions with piecewise-constant arguments, Periodica Mathematica Hungarica, 56:1 (2008) 55–69.
[44] I. Gy˝ori, F. Hartung, N. A. Mohamady, On a nonlinear delay population model, Applied Mathematics and Computation, 270 (2015) 909—925.
[45] I. Gy˝ori, F. Hartung, N. A. Mohamady, Existence and uniqueness of positive solutions of a system of nonlinear algebraic equations, Period. Math. Hung., DOI 10.1007/s10998-016-0179-3, 2016.
[46] I. Gy˝ori, F. Hartung, N. A. Mohamady, Boundedness of Positive Solutions of a System of Nonlinear Delay Differential Equations, to appear in Discrete and Continuous Dynamical Systems- Series B.
[47] K.P. Hadeler, Delay equations in biology, In: Functional Differential Equations and Appl. to Fixed Points, Lect. Notes in Math. 730 (H.-O. Peitgen and H.-O.
Walther, eds.), Springer, Berlin, (1979) 136–163.
[48] K.P. Hadeler, G. Bocharov, Where to put delays in population models, in par-ticular in the neutral case, Can. Appl. Math. Q., 11:2 (2003) 159–173.
[49] T.G. Hallam, A.L. Simon ed., Mathematical Ecology: An Introduction (Springer-Verlag, 1986)
[50] J. J. Hopfield, Neurons with graded response have collective computational properties like those of two-stage neurons, Proc. Nat. Acad. Sci. U.S.A., 81 (1984) 3088–3092.
[51] J. Huang, J. Liu, G. Zhou, Stability of impulsive Cohen–Grossberg neural networks with time-varying delays and reaction-diffusion terms, Abstr. Appl.
Anal., 2013 Article ID 409758, (2013) 1–10.
[52] G.E. Hutchinson, Circular causal systems in ecology, Ann. NY Acad. Sci., 50 (1948) 221-246.
[53] C.C. Hwang, C.J. Cheng, T.L. Liao, Globally exponential stability of general-ized Cohen–Grossberg neural networks with delays, Phys. Lett. A, 319 (2003) 157–166.
[54] J.A. Jacquez, C.P. Simon, Qualitative theory of compartmental systems, SIAM Rev., 35(1) (1993) 43–79.
[55] J.A. Jacquez, C.P. Simon, Qualitative theory of compartmental systems with lags, Math. Biosci., 180 (2002) 329–362.
[56] M. Kaykobad, Positive solutions of positive linear systems, Linear Algebra Appl., 64 (1985) 133–140.
[57] Y. Kuang, Delay Differential Equations with Applications in Population Dy-namics, Academic Press, Boston, MA, 1993.
[58] W.T. Li, G. Lin, S. Ruan, Existence of travelling wave solutions in delayed reaction-diffusion systems with applications to diffusion-competition systems, Nonlinearity, 19 (2006) 1253–1273
[59] B. Liu, Global stability of a class of Nicholson’s blowflies model with patch structure and multiple time-varying delays, Nonlinear Anal. Real World Appl, 11 (2010) 2557-2562.
[60] N. MacDonald, Time Lags in Biological Models, (Berlin:Springer, 1978) [61] Y. Muroya, Permanence, contractivity and global stability in logistic equations
with general delays, J. Math. Anal. Appl. 302(2) (2005) 389–401.
[62] P. Nelson, Positive solutions of positive linear equations, Proc. Amer. Math.
Soc., 31(2) (1972) 453–457.
[63] L. Nie, Z. Tenga, L. Hua, J. Peng, Qualitative analysis of a modified Leslie–
Gower and Holling-type II predator-prey model with state dependent impulsive effects, Nonlinear Anal. Real World Appl., 11 (2010) 1364–1373.
[64] R.M. Nisbet, W.S.C. Gurney, Modelling Fluctuating Populations, Wiley, Chich-ester, 1982.
[65] J.F. Perez, C.P. Malta and F.A.B. Coutinho, Qualitative analysis of oscillations in isolated populations of flies, J. Theor. Biol., 71 (1978), 505–514.
[66] S. Ruan, Delay differential equations in single species dynamics, in O. Arino, H.L. Hbid, E. Ait Dads (eds.), Delay Differential Equations and Applications, Springer, Berlin, 2006, pp.477–517.
[67] L. Wang, H. Zhao, J. Cao, Synchronized bifurcation and stability in a ring of diffusively coupled neurons with time delay, Neural Networks 75 (2016) 32–46.
[68] J. Wiener, Differential equations with piecewise constant delays, Trends in the Theory and Practice of Nonlinear Differential Equations, ed. V. Lakshmikan-tham, Marcel Dekker, (1983) 547–552.
[69] J. Wiener, Generalized Solutions of Functional Differential Equations, World Scientific, Singapore, 1993.
[70] Y. Yang, J.H. Zhang, Existence results for a nonlinear system with a parameter, J. Math. Anal. Appl., 340 (2008) 658–668.
[71] Y. Yang, J. Zhang, Existence and multiple solutions for a nonlinear system with a parameter, Nonlinear Anal., 70(7) (2009) 2542–2548.
[72] Yu.V. Utyupin, L.V. Nedorezov, About a model of population dynamics with time lag in birth process, Population Dynamics: Analysis, Modelling, Forecast, 3(1) (2014) 25–37.
[73] G. Zhang, Existence of non-zero solutions for a nonlinear system with a param-eter, Nonlinear Anal., 66 (2007) 1410–1416.
[74] G. Zhang, L. Bai, Existence of solutions for a nonlinear algebraic system. Dis-cret, Dyn. Nat. Soc., 2009 (2009) 1–28.
[75] G. Zhang, S.S. Cheng, Existence of solutions for a nonlinear system with a parameter, J. Math. Anal. Appl., 314(10) (2006) 311–319.
[76] G. Zhang, W. Feng, On the number of positive solutions of a nonlinear algebraic system, Linear Alg. Appl., 422 (2007) 404–421.
In this Appendix, we give some proofs of some of our results.