5 papers · 1 filter
Delayed Pattern Formation in Two-Dimensional Domains
Nirmali Prabha Das, István Balázs, Bornali Das +1
This study investigates how the interaction between gene expression time delay and domain size governs spatio-temporal pattern formation in a reaction-diffusion system. To investig…
Morse decomposition for semi-dynamical systems with an application to systems of state-dependent delay differential equations
István Balázs, Ábel Garab, Teresa Rauscher
Understanding the structure of the global attractor is crucial in the field of dynamical systems, where Morse decompositions provide a powerful tool by partitioning the attractor i…
Discrete Lyapunov functional for cyclic systems of differential equations with time-variable or state-dependent delay
István Balázs, Ábel Garab
We consider nonautonomous cyclic systems of delay differential equations with variable delay. Under suitable feedback assumptions, we define an (integer valued) Lyapunov functional…
A continuous semiflow on a space of Lipschitz functions for a differential equation with state-dependent delay from cell biology
István Balázs, Philipp Getto, Gergely Röst
We establish variants of existing results on existence, uniqueness and continuous dependence for a class of delay differential equations (DDE). We apply these to continue the analy…
Hopf bifurcation and period functions for Wright type delay differential equations
István Balázs, Gergely Röst
We present the simplest criterion that determines the direction of the Hopf bifurcations of the delay differential equation , as the parameter passes through…