Bifurcation Analysis of the Oregonator Model in the 3-D Space Bromate/Malonic Acid/Stoichiometric Coefficient

Mazzotti, Marco; Morbidelli, Massimo; Serravalle, G.

doi:10.1021/j100013a020

Cited by 15 publications

(11 citation statements)

References 4 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…These simulations also revealed that the area of coexistence depends on the value of the parameter f. As seen in Figure 8.7, the coexistence area in the both responsive and nonresponsive heterogeneous 1D gels disappears as the stoichiometric parameter f is increased. The observed hysteretic effect takes place because the Oregonator model exhibits the subcritical Hopf bifurcation at the values of the stoichiometric parameter of f < 1 [39]. Figure 8.7 also shows that the responsive gels exhibit smaller hysteresis than the nonresponsive samples.…”

Section: Straining Heterogeneous Bz Gelsmentioning

confidence: 88%

Self‐Oscillating Gels as Biomimetic Soft Materials

Kuksenok

Yashin

Dayal

et al. 2010

Nonlinear Dynamics With Polymers

View full text Add to dashboard Cite

IntroductionOne of the hallmarks of living systems is irritability, the ability to sense, and respond to a potentially harmful stimulus. The most characteristic response in biological systems to such a threat is to simply move away. For example, the leaves of a mimosa plant fold away from the touch of a hand, and the same hand pulls away from a flame. One of the challenges in designing synthetic biomimetic systems that exhibit analogous behavior is creating macroscopic objects that not only sense an ''adverse'' condition but also undergo autonomous, directed motion in the presence of this condition. Recently, we have developed theoretical and computational models [1-3] for chemoresponsive polymer gels and, through these models, have been attempting to design such adaptive systems. Our efforts have focused on a particular class of responsive gels, namely, those undergoing the Belousov-Zhabotinsky (BZ) reaction [4]. As we show below, by harnessing the inherent properties of these polymer networks, we can design materials that emit a chemical ''alarm signal'' and directed motion in response to a mechanical deformation or impact [5]. We can also design a polymeric ''worm'' that moves away from light of a certain wavelength, which is an adverse stimulus for the BZ reaction [6].The unique attributes of BZ gels make them ideal candidates for displaying biomimetic behavior, that is, these polymer networks can expand and contract periodically without external stimuli. This autonomous, self-oscillatory behavior is due to a ruthenium catalyst that is covalently bonded to the polymers [7-24]. The BZ reaction generates a periodic oxidation and reduction of the anchored metal ion, which changes the hydrophilicity of the polymer chains, and in this manner the chemical oscillations induce the rhythmic swelling and deswelling in the gel [7][8][9][10][11][12][13][14][15][16][17][18][19][20][21][22][23][24]. In other words, the chemical energy from BZ reaction fuels the mechanical oscillations of these gels. These self-oscillating gels can perform sustained work until the reagents in the host solution are consumed and can be simply ''refueled'' by replenishing these solutes. Millimeter-sized pieces of the BZ gels can actually Nonlinear Dynamics with Polymers: Fundamentals, Methods and Applications. Edited by John A. Pojman and Qui Tran-Cong-Miyata

show abstract

Section: Straining Heterogeneous Bz Gelsmentioning

confidence: 88%

Self‐Oscillating Gels as Biomimetic Soft Materials

Kuksenok

Yashin

Dayal

et al. 2010

Nonlinear Dynamics With Polymers

View full text Add to dashboard Cite

show abstract

“…The rate equations are numerically solved using the calculated value of H = 0.9 M and f = 1.6 . The values of rate constants inherent to the traditional three variable Oregonator model are taken as k 1 = 2.0 H 2 M –1 s –1 , k 2 = 2.0 × 10 8 H M –1 s –1 , k 3 = 2.0 × 10 3 H M –1 s –1 , and k 4 = 4.0 × 10 8 M –1 s –1 . The rate constants for the steps R6 and R7 are taken as k 6 = 0.5 B M –1 s –1 , k 7 = 8.0 × 10 9 H M –1 s –1 , and k –7 = 2.0 × 10 –2 H M –1 s –1 .…”

Section: Methodsmentioning

confidence: 99%

“…23 The rate equations are numerically solved using the calculated value 38 of H = 0.9 M and f = 1.6. 6 The values of rate constants inherent to the traditional three variable Oregonator model are taken as 39…”

Section: ■ Introductionmentioning

confidence: 99%

Fast-Moving Self-Propelled Droplets of a Nanocatalyzed Belousov–Zhabotinsky Reaction

2021

View full text Add to dashboard Cite

Self-sustained locomotion by virtue of an internalized chemical reaction is a characteristic feature of living systems and has inspired researchers to develop such self-moving biomimetic systems. Here, we harness a self-oscillating Belousov–Zhabotinsky (BZ) reaction, a well-known chemical oscillator, with enhanced kinetics by virtue of our graphene-based catalytic mats, to elucidate the spontaneous locomotion of BZ reaction droplets. Specifically, our nanocatalysts comprise ruthenium nanoparticle decorations on graphene oxide, reduced graphene oxide, and graphene nanosheets, thereby creating 0D–2D heterostructures. We demonstrate that when these nanocatalyzed droplets of the BZ reaction are placed in an oil-surfactant medium, they exhibit a macroscopic translatory motion at the velocities of few millimeters per second. This motion is brought about by the combination of enhanced kinetics of the BZ reaction and the Marangoni effect. Our investigations reveal that the velocity of locomotion increases with the electrical conductivity of our nanocomposites. Moreover, we also show that the positive feedback generated by the reaction–diffusion phenomena results in an asymmetric distribution of surface tension that, in turn, facilitates the self-propelled motion of the BZ droplets. Finally, we explore a system of multiple nanocatalyzed BZ droplets and reveal a variety of motions caused by their mutual interactions. Our findings suggest that through the use of 0D–2D hybrid nanomaterials, it is possible to design fast-moving self-propelled synthetic objects for a variety of biomimetic applications.

show abstract

“…48 NM is derived from OM following the same steps for the Oregonator system described in Ref. 52, based on the definitions of the scaled variables given in Table 3. The ODE system for NM is given in Table 2.…”

Section: Derivation Of Nm From Ommentioning

confidence: 99%

“…Details are given in Appendix D. Equations of the RM are listed inTable 2. In the derivation of RM from NM we follow the same steps as was done for the Oregonator model 52. …”

mentioning

confidence: 99%

Mathematical Modeling of Behçet's Disease: A Dynamical Systems Approach

et al. 2015

View full text Add to dashboard Cite

Behçet's Disease (BD) is a multi-systemic, auto-inflammatory disorder that is characterized by recurrent episodes of inflammatory manifestations affecting skin, mucosa, eyes, blood vessels, joints and several other organs. BD is classified as a multifactorial disease with an important contribution of genetics. Genetic studies suggest that there is a strong association of BD with a Class I major histocompatibility complex antigen, named HLA-B*51, along with several other weaker associations with genes encoding proteins involved in inflammation. However, pathogenic mechanisms associated with these genetic variations and their interactions with the environment have not been elucidated yet. In this paper, we present a mathematical model for BD based on a dynamical systems perspective that captures especially the relapsing nature of the disease. We propose a disease progression mechanism and construct a model, in the form of coupled ordinary differential equations (ODEs), which reveals the occurrence pattern of the disease in the population. According to our model, the disease has three distinct modes describing different phenotypes of people carrying HLA-B*51 tissue antigen, namely, the Healthy Carrier, the Potential Patient and the Active Patient. We herein present an exemplary mathematical model for BD, for the first time in the literature, that concisely captures the actions of many cell types together with genetic and environmental effects. The proposed model provides insight into this complex inflammatory disease which may lead to identification of new tools for its treatment and prevention.

show abstract

Bifurcation Analysis of the Oregonator Model in the 3-D Space Bromate/Malonic Acid/Stoichiometric Coefficient

Cited by 15 publications

References 4 publications

Self‐Oscillating Gels as Biomimetic Soft Materials

Self‐Oscillating Gels as Biomimetic Soft Materials

Fast-Moving Self-Propelled Droplets of a Nanocatalyzed Belousov–Zhabotinsky Reaction

Mathematical Modeling of Behçet's Disease: A Dynamical Systems Approach

Contact Info

Product

Resources

About