Pursuit-evasion predator-prey waves in two spatial dimensions

We consider a spatially distributed population dynamics model with excitable predator-prey dynamics, where species propagate in space due to their taxis with respect to each other's gradient in addition to, or instead of, their diffusive spread. Earlier, we have described new phenomena in this model in one spatial dimension, not found in analogous systems without taxis: reflecting and self-splitting waves. Here we identify new phenomena in two spatial dimensions: unusual patterns of meander of spirals, partial reflection of waves, swelling wavetips, attachment of free wave ends to wave backs, and as a result, a novel mechanism of self-supporting complicated spatio-temporal activity, unknown in reaction-diffusion population models.Comment: 15 pages, 15 figures, submitted to Chao

Quasisolitons in self-diffusive excitable systems, or Why asymmetric diffusivity does not violate the Second Law

Solitons, defined as nonlinear waves which can reflect from boundaries or transmit through each other, are found in conservative, fully integrable systems. Similar phenomena, dubbed quasi-solitons, have been observed also in dissipative, "excitable" systems, either at finely tuned parameters (near a bifurcation) or in systems with cross-diffusion. Here we demonstrate that quasi-solitons can be robustly observed in excitable systems with excitable kinetics and with self-diffusion only. This includes quasi-solitons of fixed shape (like KdV solitons) or envelope quasi-solitons (like NLS solitons). This can happen in systems with more than two components, and can be explained by effective cross-diffusion, which emerges via adiabatic elimination of a fast but diffusing component. We describe here a reduction procedure can be used for the search of complicated wave regimes in multi-component, stiff systems by studying simplified, soft systems.Comment: 11 pages, 2 figures, as accepted to Scientific Reports on 2016/07/0

Soliton-like phenomena in one-dimensional cross-diffusion systems: a predator-prey pursuit and evasion example

We have studied properties of nonlinear waves in a mathematical model of a predator-prey system with pursuit and evasion. We demonstrate a new type of propagating wave in this system. The mechanism of propagation of these waves essentially depends on the ``taxis'', represented by nonlinear ``cross-diffusion'' terms in the mathematical formulation. We have shown that the dependence of the velocity of wave propagation on the taxis has two distinct forms, ``parabolic'' and ``linear''. Transition from one form to the other correlates with changes in the shape of the wave profile. Dependence of the propagation velocity on diffusion in this system differs from the square-root dependence typical of reaction-diffusion waves. We demonstrate also that, for systems with negative and positive taxis, for example, pursuit and evasion, there typically exists a large region in the parameter space, where the waves demonstrate quasisoliton interaction: colliding waves can penetrate through each other, and waves can also reflect from impermeable boundaries.Comment: 15 pages, 18 figures, submitted to Physica

Envelope quasisolitons in dissipative systems with cross-diffusion

Copyright © 2011 American Physical SocietyJournal ArticleWe consider two-component nonlinear dissipative spatially extended systems of reaction-cross-diffusion type. Previously, such systems were shown to support "quasisoliton" pulses, which have a fixed stable structure but can reflect from boundaries and penetrate each other. Herein we demonstrate a different type of quasisolitons, with a phenomenology resembling that of the envelope solitons in the nonlinear Schrödinger equation: spatiotemporal oscillations with a smooth envelope, with the velocity of the oscillations different from the velocity of the envelope

Classification of wave regimes in excitable systems with linear cross diffusion

Copyright © 2014 American Physical SocietyWe consider principal properties of various wave regimes in two selected excitable systems with linear cross diffusion in one spatial dimension observed at different parameter values. This includes fixed-shape propagating waves, envelope waves, multienvelope waves, and intermediate regimes appearing as waves propagating at a fixed shape most of the time but undergoing restructuring from time to time. Depending on parameters, most of these regimes can be with and without the "quasisoliton" property of reflection of boundaries and penetration through each other. We also present some examples of the behavior of envelope quasisolitons in two spatial dimensions.Russian Foundation for Basic Research (RFBR

Інноваційна модернізація економіки як основа реалізації національних економічних інтересів

The need for this study can be explained by the fact that the solution of the problems in the development of the system of management that have emerged under critical conditions of permanent political and economic instability, institutional uncertainty requires the development of the system of measures aimed at engaging driving forces of economic transformation. The basis for such social transformation is the implementation of social–economic transformations of efficient models of the ratio of economic interests and innovative modernization of economy as the basis for their achievements.  The aim of the research is revealing the role of the innovative modernization of the economy in the formation and implementation of the national economic interests. The methods of scientific research are abstract–logical, statistical, induction and deduction. Based on the evaluation of activation of the driving forces of economic transformation, we defined the need for implementing in the transformation practice of the efficient models of formation of economic interests. The necessity was substantiated of the formation and development of the innovative modernization of the economy as a basis for achieving the level of competitiveness of the national economic system, adequate to the goals and needs of the transformational period under conditions of growing global competition. We proposed the ways of reconciling the economic interests of representatives of business structures with the national economic interests of Ukraine. The article reveals the role of the state in creating the institutional environment, the most efficient forms and methods of economic management of innovative modernization of the national economy were determined. We proposed the measures to consolidate the efforts of all the participants of the innovative modernization of the economy, which imply a synthesis of the provisions of the neoclassical and Keynesian doctrine with the activities of the state, adapted to modern realities of Ukraine, the mechanisms of self––regulation of the market. In subsequent research it is suggested to implement the development of the institutional environment of competing economic interests of economic entities, to motivate them to engage into activities in the field of new technologies

Effect of biogenic polyamines on sliding motility of mycobacteria in the presence of antibiotics

Nowadays, sliding is the least investigated mode of bacterial motility. Sliding is a process of passive movement on the surface of semi-liquid mediums which was originally described for mycobacteria and other bacterial species deprived of the organelles specialized for movement. Some mycobacteria are able to colonize surfaces, including tissues of macro-organisms, using glycopeptidolipids localized in the cell envelope for this aim. This is a serious problem for effective therapy of mycobacteriosis caused by nontuberculosis mycobacteria. Furthermore, animal tissues contain biogenic polyamines, which can increase tolerance of microorganisms to stresses, including antibiotics, and modulate cell motility. Therefore, studying mutual effects of biogenic polyamines and antibiotics on the expansion of mycobacteria is important for medicine. Mycobacterial strains, including the parent Mycolicibacterium smegmatis mc2 155 and strains containing single (ΔrelMsm) or double (ΔrelMsmΔrelZ) deletions, were used as the objects of this study. The content of glycopeptidolipids was determined using thin layer chromatography. Sliding motility was assessed by measuring the area of the sliding colony. The effectiveness of antibiotics was measured by comparison of the areas of sliding colonies in the presence of comparable concentrations of antibiotics. The polyamines spermidine and spermine had different effects on the sliding of mycobacteria through an increase or decrease in the colony areas. At the same time, polyamines had neither bactericidal nor bacteriostatic effects. The polyamines contained in the medium decreased the bactericidal effects of the antibiotics streptomycin or isoniazid, but enhanced the effects of DMNP, a synthetic analogue of the natural antibiotic erogorgiaene. Rifampicin was the most effective of all antibiotics investigated here. Moreover, we found that glycopeptidolipids are, apparently, not the only regulators of mycobacterial sliding