Abstract : The purpose of this minisymposium is to bring experts in delay differential and stochastic differential equations
and to discuss recent advancement in the area, as well as applications of dynamical systems to emerging areas of mathematical biology, medicine and engineering. Qualitative behaviour, stability, oscillation will be the focus of theoretical investigations. In theoretical advancement, the focus is on asymptotic behaviour, in particular local and global stability, and its control. The areas of application include population dynamics, modeling brain activity, cancer treatment, and engineering.
[04596] Impacts of demographic and environmental stochasticity on population dynamics with cooperative effects
Format : Talk at Waseda University
Author(s) :
Yun Kang (Arizona State University)
Tao Feng (Yangzhou University,)
Hongjuan Zhou (Arizona State University)
Zhipeng Qiu (Nanjing University of Science and Technology)
Abstract : This work provides rigorous analysis on stochastic persistence and extinction, ergodicity, and the existence
of a nontrivial periodic solution to study the impacts of demographic and environmental stochasticity on population
dynamics with component Allee effects. We show that stochasticity may affect population dynamics differently for different strength of Allee effects. Moreover, in the extinction case, demographic and environmental stochasticity can not change the trend of population extinction, but they can delay or promote population extinction.
[03954] Recent advances in modeling tick-borne dynamics using delay differential equations
Format : Talk at Waseda University
Author(s) :
Jianhong Wu (York University)
Abstract : We provide a short survey of recent advances in modeling tick-borne disease transmission dynamics using structured population dynamics models and delay differential equations. Focus will be on those studies relevant to diapause, that
introduces additional delays in the modeling system (and periodic variation of the environment), and on co-feeding
transmission route that requires incorporation of individual infestation dynamics into the tramsmission dynamics at the population level.
[03402] Delay and Resonance: From Differential Equations to Random Walks
Format : Talk at Waseda University
Author(s) :
Toru Ohira (Graduate School of Mathematics, Nagoya University)
Abstract : Various types of oscillatory dynamics are associated with systems with delayed feedback. We present two simple models that take advantage of these oscillations to induce resonating behaviors. The first model is a simple first-order delay differential equation with a time linear coefficient. The other model is a simple stochastic binary bit with delayed feedback. Both models produce transient oscillatory dynamics that can show resonance with the tuned value of the delay.
[03310] Evolutionary Games with Strategy-Dependent Time Delays
Format : Talk at Waseda University
Author(s) :
Jacek Miękisz (University of Warsaw)
Abstract : We present a new behavior of systems with time delays. We show that in differential replicator equations with strategy-dependent time delays, interior stationary states, describing the level of cooperation in evolutionary games of social dilemmas, depend continuously on time delays, they may also disappear or additional states can emerge. A Prisoner’s Dilemma model with an asymptotically stable population with just cooperators is presented. We will also discuss some results for finite populations.
00699 (2/4) : 1D @G404 [Chair: John A. D. Appleby]
[03461] Asymptotic behaviour for nonautonomous Nicholson equations with mixed monotonicities
Format : Talk at Waseda University
Author(s) :
Teresa Faria (Professor/University of Lisbon)
Abstract : A general nonautonomous Nicholson equation with multiple pairs of distinct delays is studied. Sufficient conditions for permanence are given, with explicit lower and upper uniform bounds. Imposing an additional condition on the size of some delays, the global attractivity of positive solutions is established. Sharper results are obtained when there exists a positive equilibrium or periodic solution. These results improve on recent literature, due to the generality of the equation and less restrictive constraints.
[03291] Periodicity and stability in some biological delay models
Format : Talk at Waseda University
Author(s) :
Anatoli F Ivanov (Pennsylvania State University)
Abstract : We consider mathematical models of several biological processes which are described by simple form scalar delay differential equations. They include autonomous nonlinear equations as well as equations with periodic coefficients. New criteria for the global asymptotic stability of equilibrium states are proposed. It is proved that the instability of equilibria implies the existence of periodic motions in the models. Explicit examples from applications demonstrating theoretical findings are given.
[03816] Exponential stability of linear discrete systems with multiple delays
Format : Talk at Waseda University
Author(s) :
Josef Diblik (Brno University of Technology)
Josed Diblik (Brno University of Technology)
Abstract : The problem of exponential stability of delayed linear discrete systems with multiple delays and with constant matrices is studied. A new degenerated Lyapunov-Krasovskii functional is used to derive sufficient conditions for exponential stability and derive an exponential estimate of the norm of solutions. Though often used in the study of stability, the assumption that the spectral radius of the matrix of linear terms is less than 1 is not applied here.
[03498] On asymptotic stability of equations and systems with distributed, unbounded and infinite delays
Format : Talk at Waseda University
Author(s) :
Elena Braverman (university of Calgary)
Leonid Berezansky (Ben-Gurion University of Negev)
Abstract : Many differential equations of mathematical biology assume delayed production process and instantaneous mortality. Introduction of delay can destabilize the unique positive equilibrium and even lead to chaos. However, for some types of equations and systems, lags in the reproduction term do not change stability properties. Consideration of variable, unbounded and distributed delays emphasizes robustness of this `absolute stability' property. Influence of an infinite, not just unbounded, delay is also outlined.
[04635] Asymptotic classification of forced stochastic systems with memory
Format : Talk at Waseda University
Author(s) :
John A Appleby (Dublin City University)
Emmet Lawless (Dublin City University)
Abstract : Linear stochastic functional differential equations are among the simplest stochastic systems that possess path-dependence. In recent work, the authors have characterised the asymptotic behaviour, including rates of convergence to equilibria, of solutions of such systems which are not externally forced. In this work, we are able to characterise the asymptotic behaviour of state-independent forcing terms which guarantee specified types of asymptotic rates of decay, growth and fluctuation size, of solutions.
[04851] Asymptotic analysis of stochastic functional differential equations
Format : Talk at Waseda University
Author(s) :
Emmet Lawless (Dublin City University)
John Appleby (Dublin City University)
Abstract : In this talk we are concerned with the asymptotic behaviour of the mean square of scalar stochastic functional differential equations with finite delay. We are primarily interested in providing characterisations of various types of mean square stability and discussing the robustness of solutions under perturbations. Additionally, we highlight how our methods of proof can be utilised to make progress in understanding the mean square behaviour of equations of Volterra type.
[03977] An order-one adaptive scheme for the strong approximation of stochastic systems with jumps.
Format : Online Talk on Zoom
Author(s) :
Conall Kelly (University College Cork)
Gabriel Lord (Radboud University)
Fandi Sun (Heriot-Watt University)
Abstract : Consider a system of SDEs with coefficients that are locally Lipschitz and together satisfy a montone condition. It is known that the explicit Milstein scheme on a uniform mesh fails to converge here.
We construct an adaptive mesh to ensure order-one convergence that reduces the stepsize as solutions approach the boundary of a sphere, and modify it for systems additionally perturbed by Poisson jumps.
We demonstrate our scheme in the modelling of telomere length dynamics.
[02373] Mathematical Model of Hepatitis B Virus Combination Treatment
Format : Online Talk on Zoom
Author(s) :
Irina Volinsky (Ariel University, Israel)
Abstract : HBV has a high mortality rate with respect to other common known diseases. The commonly used cure for chronic HBV cases is the fusion of interferon and analogous nucleoside methods. The addition of IL-2 therapy proposed in this article. This method was validated to be highly effective. This model will take into account the response of the immune system of the patient and will use immune therapy as a support.
[04297] The Impact of Time Delays on Synchrony in a Neural Field Model
Format : Online Talk on Zoom
Author(s) :
Sue Ann Campbell (University of Waterloo)
Isam Al-Darabsah (Jordan University of Science and Technology)
Bootan Rahman (University of Kurdistan Hewler (UKH))
Wilten Nicola (University of Calgary)
Liang Chen (University of Waterloo)
Abstract : We consider a network of Wilson-Cowan nodes with homeostatic adjustment of the inhibitory coupling strength and time delayed, excitatory coupling. Without delay, the system exhibits rich dynamics including oscillations, mixed-mode oscillations, and chaos. We show that Hopf bifurcations induced by the excitatory coupling, the connectivity structure and the delay lead to different phase-locked oscillations: both synchronized and desynchronized. We show that interaction between different Hopf bifurcations can lead to complex solutions, such as intermittent synchronization.
[03295] Stability analysis of coupled feedback in hematopoiesis
Format : Talk at Waseda University
Author(s) :
Jacques Bélair (Université de Montréal)
Abstract : Hematopoiesis, the production of mammalian blood cells, involves an intertwined network of physiological processes, with nonlinear, delayed feedback control mechanisms. We consider a simplified model of the coupled regulation of erythrocytes (red blood cells) and thrombocytes (platelets).
Equilibrium solutions are determined, their stability established and the nature of the oscillations when instability occurs are investigated. The mathematical part of the analysis revolves around a transcendental characteristic equation of second order with two delays.
