Stabilization strategies for some reaction–diffusion systems

A two-component reaction–diffusion system is considered. The question of stabilizing to zero one of the components of the solution via an internal control acting on a small subdomain and preserving nonnegativity of both components is investigated. Our results apply to predator–prey systems.     

Viktor Anatol’evich Akulichev (On his 70th birthday)

Acoustical Physics -     

Influence of most important radicals on the numerically simulated belousov-zhabotinsky oscillatory reaction under batch conditions

In the already proposed model of the Belousov-Zhabotinsky reaction with the Br₂O species as intermediate one, the reactions with malonyl (MA^·), bromomalonyl (BrMA^·) and tartronyl (TA^·) radicals were introduced with aim to explore their role in overall dynamics. The related numerical simulations of the experimentally obtained dynamic states under batch conditions were successfully performed.     

Activity of polymer supported cobalt catalyst in the Bray-Liebhafsky oscillator

The infuence of poly-4-vinylpyridine-co-divinylbenzene-Co²⁺ catalyst on the Bray-Liebhafsky (BL) oscillator used as the matrix for establishing catalyst’s activity was analyzed. The addition of the catalyst do not change the dynamics of the reaction in the BL matrix, but the periods of the oscillatory evolution as well as the preoscillatory period (τ₁) and the duration from the beginning of the reaction to the end of the oscillatory state (τ_end). All experimental results are simulated satisfactory. The article is published in the original.     

Dynamic behavior of the bray-liebhafsky oscillatory reaction controlled by sulfuric acid and temperature

The non-periodic, periodic and chaotic regimes in the Bray-Liebhafsky (BL) oscillatory reaction observed in a continuously fed well stirred tank reactor (CSTR) under isothermal conditions at various inflow concentrations of the sulfuric acid were experimentally studied. In each series (at any fixed temperature), termination of oscillatory behavior via saddle loop infinite period bifurcation (SNIPER) as well as some kind of the Andronov-Hopf bifurcation is presented. In addition, it was found that an increase of temperature, in different series of experiments resulted in the shift of bifurcation point towards higher values of sulfuric acid concentration.     

Versatile binding properties of a di-2-pyridyl ketone nicotinoylhydrazone ligand: crystal structure of a Cu(II) complex

Six new copper complexes of di-2-pyridyl ketone nicotinoylhydrazone (HDKN) have been synthesized. The complexes have been characterized by a variety of spectroscopic techniques and the structure of [Cu(DKN)(2)]·H(2)O has been determined by single crystal X-ray diffraction. The compound [Cu(DKN)(2)]·H(2)O crystallized in the monoclinic space group P2(1) and has a distorted octahedral geometry. The IR spectra revealed the presence of variable modes of chelation for the investigated ligand. The EPR spectra of compounds [Cu(2)(DKN)(2)(μ-N(3))(2)] and [Cu(2)(DKN)(2)(μ-NCS)(2)] in polycrystalline state suggest a dimeric structure as they exhibited a half field signal, which indicate the presence of a weak interaction between two Cu(II) ions in these complexes.     

Structures of chaos in open reaction systems

By numerically simulating the Bray-Liebhafsky (BL) reaction (the hydrogen peroxide decomposition in the presence of hydrogen and iodate ions) in a continuously fed well stirred tank reactor (CSTR), we find "structured" types of chaos emerging in regular order with respect to flow rate as the control parameter. These chaotic "structures" appear between each two successive periodic states, and have forms and evolution resembling to the neighboring periodic dynamics. More precisely, in the transition from period-doubling route to chaos to the arising periodic mixture of different mixed-mode oscillations, we are able to recognize and qualitatively and quantitatively distinguish the sequence of "period-doubling" chaos and chaos consisted of mixed-mode oscillations (the "mixed-mode structured" chaos), both appearing in regular order between succeeding periodic states. Additionally, between these types of chaos, the chaos without such recognizable "structures" ("unstructured" chaos) is also distinguished. Furthermore, all transitions between two successive periodic states are realized through bifurcation of chaotic states. This scenario is a universal feature throughout the whole mixed-mode region, as well as throughout other mixed-mode regions obtained under different initial conditions.     

Temperature dependence of catalytic cyclohexane partial oxidation in a polytetrafluoroethylene reactor

Polymer-supported Co(II) catalyst was prepared and its activity and selectivity in the partial oxidation of cyclohexane was determined at several temperatures in a polytetrafluoroethylene reactor (PTFE). The catalyst was characterized by means of SEM-EDX, FTIR, diffuse reflectance UV-Vis, N₂ sorption, and mecury porosimetry. Activation energies were determined under steady state conditions for the net production of cyclohexanone and cyclohexanol and for cyclohexane and oxygen net consumption. Some activation energies were lower than the ones reported for the uncatalyzed process, indicating that the catalyst played an important role in the initiation of the free-radical reaction. The text was submitted by the authors in English.     

The multicomponent reaction of dimethoxycarbene, dimethyl butynedioate and electrophilic styrenes: an unprecedented synthesis of highly substituted cyclopentenone acetals

The zwitterionic species generated by the addition of dimethoxycarbene to dimethyl butynedioate is trapped by arylidenemalononitrile to yield cyclopentenone derivatives.     

Feedback Stabilization for a Reaction-Diffusion System with Nonlocal Reaction Term

We consider a two-component reaction-diffusion system with a nonlocal reaction term. A necessary condition and a sufficient condition for the internal stabilizability to zero of one of the two components of the solution while preserving the nonnegativity of both components have been established in [6 S. Ani?a , W.-E. Fitzgibbon , and M. Langlais ( 2009 ). Global existence and internal stabilization for a class of predator-prey systems posed on non coincident spatial domains . Discrete Cont. Dynam. Syst. B 11 : 805 – 822 .[Crossref], [Web of Science ®] , [Google Scholar]]. In case of stabilizability, a feedback stabilizing control of harvesting type has been indicated. The rate of stabilization (for the indicated feedback control) is given by the principal eigenvalue of a certain non-selfadjoint operator. A large principal eigenvalue leads to a fast stabilization. The first main goal of this article is to approximate this principal eigenvalue. This is done in two steps. First, we investigate the large-time behavior of the solution to a logistic population dynamics with migration, and next we derive as a consequence a method to approximate the principal eigenvalue. The other main goal is to derive a conceptual iterative algorithm to improve the position of the support of the control in order to get a faster stabilization. Our results apply to prey-predator systems.