Delay and periodicity Export

@article{citeulike:5227450, abstract = {Systems with time delay play an important role in modeling of many physical and biological processes. In this paper we describe generic properties of systems with time delay, which are related to the appearance and stability of periodic solutions. In particular, we show that delay systems generically have families of periodic solutions, which are reappearing for infinitely many delay times. As delay increases, the solution families overlap leading to increasing coexistence of multiple stable as well as unstable solutions. We also consider stability issue of periodic solutions with large delay by explaining asymptotic properties of the spectrum of characteristic multipliers. We show that the spectrum of multipliers can be split into two parts: pseudocontinuous and strongly unstable. The pseudocontinuous part of the spectrum mediates destabilization of periodic solutions.}, author = {Yanchuk, S. and Perlikowski, P.}, citeulike-article-id = {5227450}, citeulike-linkout-0 = {http://scitation.aip.org/getabs/servlet/GetabsServlet?prog=normal&id=PLEEE8000079000004046221000001&idtype=cvips&gifs=yes}, citeulike-linkout-1 = {http://link.aps.org/abstract/PRE/v79/e046221}, citeulike-linkout-2 = {http://dx.doi.org/10.1103/PhysRevE.79.046221}, doi = {10.1103/PhysRevE.79.046221}, journal = {Physical Review E (Statistical, Nonlinear, and Soft Matter Physics)}, keywords = {dynamics, mathematics, one-of-these-days}, number = {4}, pages = {046221+}, posted-at = {2009-07-22 12:09:46}, priority = {2}, publisher = {APS}, title = {Delay and periodicity}, url = {http://dx.doi.org/10.1103/PhysRevE.79.046221}, volume = {79}, year = {2009} }

TY - JOUR ID - citeulike:5227450 L3 - citeulike-article-id:5227450 N2 - Systems with time delay play an important role in modeling of many physical and biological processes. In this paper we describe generic properties of systems with time delay, which are related to the appearance and stability of periodic solutions. In particular, we show that delay systems generically have families of periodic solutions, which are reappearing for infinitely many delay times. As delay increases, the solution families overlap leading to increasing coexistence of multiple stable as well as unstable solutions. We also consider stability issue of periodic solutions with large delay by explaining asymptotic properties of the spectrum of characteristic multipliers. We show that the spectrum of multipliers can be split into two parts: pseudocontinuous and strongly unstable. The pseudocontinuous part of the spectrum mediates destabilization of periodic solutions. IS - 4 JF - Physical Review E (Statistical, Nonlinear, and Soft Matter Physics) TI - Delay and periodicity PB - APS VL - 79 SP - 046221 KW - dynamics KW - mathematics KW - one-of-these-days AU - Yanchuk, S AU - Perlikowski, P PY - 2009/// UR - http://dx.doi.org/10.1103/PhysRevE.79.046221 ER -