The Oregonator system, consisting of three Ordinary Differential Equations (ODEs), can be used for modeling the Belousov-Zhabotinsky (BZ) chemical reaction. The behavior of this phenomenon is interesting, given the oscillatory character of the related chemical components. For this reason, the use of techniques such as Exponential Fitting (EF) can be very effective in solving the Oregonator system, and D’Ambrosio et. al. have conducted studies related to this purpose. In fact, given the oscillation experimental frequency of the components, they used adapted numerical methods to follow the qualitative a-priori known behavior of the solution. In a recent work, Budroni et. al. considered a modified version of the Oregonator model, inserting an additional ODE within the original system and slightly altering the others. This version was used to model a network of diffusively coupled inorganic oscillators, confined in micro-compartments by means of a flow-focus microfluidic technique. Such networks allow to understand and predict the communication modalities between different individuals, regulated by the exchange of activatory or inhibitory signals. However, there are some compartmentalization constraints that can affect the communication between consecutive micro-oscillators. Therefore, in order to improve the model from this point of view, we have introduced a constant time delay inside the coupling term of the ODEs system. We show how the new Delay Differential Equations (DDEs) model thus obtained can be used not only to quantitatively improve the correspondence between numerical and in-silico experimental results, but also to represent other types of real phenomena. In fact, as the delay varies, different synchronization scenarios occur for the micro-oscillators involved in the system. For example, there are similarities between the observed phase transition dynamics and synchronization scenarios characterizing the coordination of oscillatory limb movements. Furthermore, we analyze and compare the efficiency of numerical methods used to solve the DDEs system, also discussing techniques that can be used to improve experimental results.
Synchronization scenarios due to the insertion of time delay in a communication ODEs model for chemical oscillators
Conte Dajana;Pagano Giovanni
;Paternoster Beatrice;
2021-01-01
Abstract
The Oregonator system, consisting of three Ordinary Differential Equations (ODEs), can be used for modeling the Belousov-Zhabotinsky (BZ) chemical reaction. The behavior of this phenomenon is interesting, given the oscillatory character of the related chemical components. For this reason, the use of techniques such as Exponential Fitting (EF) can be very effective in solving the Oregonator system, and D’Ambrosio et. al. have conducted studies related to this purpose. In fact, given the oscillation experimental frequency of the components, they used adapted numerical methods to follow the qualitative a-priori known behavior of the solution. In a recent work, Budroni et. al. considered a modified version of the Oregonator model, inserting an additional ODE within the original system and slightly altering the others. This version was used to model a network of diffusively coupled inorganic oscillators, confined in micro-compartments by means of a flow-focus microfluidic technique. Such networks allow to understand and predict the communication modalities between different individuals, regulated by the exchange of activatory or inhibitory signals. However, there are some compartmentalization constraints that can affect the communication between consecutive micro-oscillators. Therefore, in order to improve the model from this point of view, we have introduced a constant time delay inside the coupling term of the ODEs system. We show how the new Delay Differential Equations (DDEs) model thus obtained can be used not only to quantitatively improve the correspondence between numerical and in-silico experimental results, but also to represent other types of real phenomena. In fact, as the delay varies, different synchronization scenarios occur for the micro-oscillators involved in the system. For example, there are similarities between the observed phase transition dynamics and synchronization scenarios characterizing the coordination of oscillatory limb movements. Furthermore, we analyze and compare the efficiency of numerical methods used to solve the DDEs system, also discussing techniques that can be used to improve experimental results.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
