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29-501: [REDACTED] Look up kinesis in Wiktionary, the free dictionary. Kinesis may refer to: Kinesis (biology) , a movement or activity of a cell or an organism in response to a stimulus Kinesis (band) , an alternative rock band from Bolton, England Kinesis (genus) , a genus of earwigs Kinesis (keyboard) , a line of ergonomic computer keyboards Kinesis (magazine) ,

58-557: A Turing bifurcation to a globally patterned state with a dominant finite wave number. The latter in two spatial dimensions typically leads to stripe or hexagonal patterns. For the Fitzhugh–Nagumo example, the neutral stability curves marking the boundary of the linearly stable region for the Turing and Hopf bifurcation are given by If the bifurcation is subcritical, often localized structures ( dissipative solitons ) can be observed in

87-413: A front-antifront pair) are unstable. For c = 0 , there is a simple proof for this statement: if u 0 ( x ) is a stationary solution and u = u 0 ( x ) + ũ ( x , t ) is an infinitesimally perturbed solution, linear stability analysis yields the equation With the ansatz ũ = ψ ( x )exp(− λt ) we arrive at the eigenvalue problem of Schrödinger type where negative eigenvalues result in

116-579: A magazine published by Vancouver Status of Women Motion, change or activity in Aristotelian philosophical concepts of potentiality and actuality Kinesis Industry , a manufacturer of bicycle frames and components Kinesis Industry , a holdings company for Kinesis Recruitment and Kinesis Property Amazon Kinesis , a real-time data processing platform provided by Amazon Web Services See also [ edit ] Kinetic (disambiguation) Kinetics (disambiguation) Topics referred to by

145-433: A nerve. Here, d u , d v , τ , σ and λ are positive constants. When an activator-inhibitor system undergoes a change of parameters, one may pass from conditions under which a homogeneous ground state is stable to conditions under which it is linearly unstable. The corresponding bifurcation may be either a Hopf bifurcation to a globally oscillating homogeneous state with a dominant wave number k = 0 or

174-408: A non-monotonic stationary solution the corresponding eigenvalue λ = 0 cannot be the lowest one, thereby implying instability. To determine the velocity c of a moving front, one may go to a moving coordinate system and look at stationary solutions: This equation has a nice mechanical analogue as the motion of a mass D with position û in the course of the "time" ξ under the force R with

203-535: A reaction diffusion differential equation holds, represents in fact a concentration variable . The simplest reaction–diffusion equation is in one spatial dimension in plane geometry, is also referred to as the Kolmogorov–Petrovsky–Piskunov equation . If the reaction term vanishes, then the equation represents a pure diffusion process. The corresponding equation is Fick's second law . The choice R ( u ) = u (1 − u ) yields Fisher's equation that

232-426: A slow movement indicates that it has found it. There are two main types of kineses, both resulting in aggregations. However, the stimulus does not act to attract or repel individuals. Orthokinesis : in which the speed of movement of the individual is dependent upon the stimulus intensity. For example, the locomotion of the collembola , Orchesella cincta , in relation to water. With increased water saturation in

261-416: A typical solution is given by travelling fronts connecting the homogeneous states. These solutions move with constant speed without changing their shape and are of the form u ( x , t ) = û ( ξ ) with ξ = x − ct , where c is the speed of the travelling wave. Note that while travelling waves are generically stable structures, all non-monotonous stationary solutions (e.g. localized domains composed of

290-438: Is different from Wikidata All article disambiguation pages All disambiguation pages Kinesis (biology) Unlike taxis, the response to the stimulus provided is non-directional. The animal does not move toward or away from the stimulus but moves at either a slow or fast rate depending on its " comfort zone ." In this case, a fast movement (non-random) means that the animal is searching for its comfort zone while

319-580: Is sometimes referred to as the Zeldovich equation as well. The dynamics of one-component systems is subject to certain restrictions as the evolution equation can also be written in the variational form and therefore describes a permanent decrease of the "free energy" L {\displaystyle {\mathfrak {L}}} given by the functional with a potential V ( u ) such that R ( u ) = ⁠ d V ( u ) / d u ⁠ . In systems with more than one stationary homogeneous solution,

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348-587: Is supposed to be the most unstable one, the Jacobian must have the signs This class of systems is named activator-inhibitor system after its first representative: close to the ground state, one component stimulates the production of both components while the other one inhibits their growth. Its most prominent representative is the FitzHugh–Nagumo equation with   f  ( u ) = λu − u − κ which describes how an action potential travels through

377-407: Is the equilibrium diffusion coefficient (defined for equilibrium r i = 0 {\displaystyle r_{i}=0} ). The coefficient α i > 0 {\displaystyle \alpha _{i}>0} characterises dependence of the diffusion coefficient on the reproduction coefficient. The models of kinesis were tested with typical situations. It

406-450: Is the population density of i th species, s {\displaystyle s} represents the abiotic characteristics of the living conditions (can be multidimensional), r i {\displaystyle r_{i}} is the reproduction coefficient, which depends on all u i {\displaystyle u_{i}} and on s , D 0 i > 0 {\displaystyle D_{0i}>0}

435-478: The Belousov–Zhabotinsky reaction , for blood clotting , fission waves or planar gas discharge systems. It is known that systems with more components allow for a variety of phenomena not possible in systems with one or two components (e.g. stable running pulses in more than one spatial dimension without global feedback). An introduction and systematic overview of the possible phenomena in dependence on

464-492: The hysteretic region where the pattern coexists with the ground state. Other frequently encountered structures comprise pulse trains (also known as periodic travelling waves ), spiral waves and target patterns. These three solution types are also generic features of two- (or more-) component reaction–diffusion equations in which the local dynamics have a stable limit cycle For a variety of systems, reaction–diffusion equations with more than two components have been proposed, e.g.

493-413: The soil there is an increase in the direction of its movement towards the aimed place. Klinokinesis : in which the frequency or rate of turning is proportional to stimulus intensity. For example, the behaviour of the flatworm ( Dendrocoelum lacteum ) which turns more frequently in response to increasing light thus ensuring that it spends more time in dark areas. The kinesis strategy controlled by

522-413: The damping coefficient c which allows for a rather illustrative access to the construction of different types of solutions and the determination of c . When going from one to more space dimensions, a number of statements from one-dimensional systems can still be applied. Planar or curved wave fronts are typical structures, and a new effect arises as the local velocity of a curved front becomes dependent on

551-641: The form of semi-linear parabolic partial differential equations . They can be represented in the general form where q ( x , t ) represents the unknown vector function, D is a diagonal matrix of diffusion coefficients , and R accounts for all local reactions. The solutions of reaction–diffusion equations display a wide range of behaviours, including the formation of travelling waves and wave-like phenomena as well as other self-organized patterns like stripes, hexagons or more intricate structure like dissipative solitons . Such patterns have been dubbed " Turing patterns ". Each function, for which

580-450: The instability of the solution. Due to translational invariance ψ = ∂ x   u 0 ( x ) is a neutral eigenfunction with the eigenvalue λ = 0 , and all other eigenfunctions can be sorted according to an increasing number of nodes with the magnitude of the corresponding real eigenvalue increases monotonically with the number of zeros. The eigenfunction ψ = ∂ x   u 0 ( x ) should have at least one zero, and for

609-437: The interest in reaction–diffusion systems is that although they are nonlinear partial differential equations, there are often possibilities for an analytical treatment. Well-controllable experiments in chemical reaction–diffusion systems have up to now been realized in three ways. First, gel reactors or filled capillary tubes may be used. Second, temperature pulses on catalytic surfaces have been investigated. Third,

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638-401: The local radius of curvature (this can be seen by going to polar coordinates ). This phenomenon leads to the so-called curvature-driven instability. Two-component systems allow for a much larger range of possible phenomena than their one-component counterparts. An important idea that was first proposed by Alan Turing is that a state that is stable in the local system can become unstable in

667-1050: The locally and instantly evaluated well-being ( fitness ) can be described in simple words: Animals stay longer in good conditions and leave bad conditions more quickly. If the well-being is measured by the local reproduction coefficient then the minimal reaction-diffusion model of kinesis can be written as follows: For each population in the biological community, ∂ t u i ( x , t ) = D 0 i ∇ ( e − α i r i ( u 1 , … , u k , s ) ∇ u i ) + r i ( u 1 , … , u k , s ) u i , {\displaystyle \partial _{t}u_{i}(x,t)=D_{0i}\nabla \left(e^{-\alpha _{i}r_{i}(u_{1},\ldots ,u_{k},s)}\nabla u_{i}\right)+r_{i}(u_{1},\ldots ,u_{k},s)u_{i},} where: u i {\displaystyle u_{i}}

696-469: The presence of diffusion . A linear stability analysis however shows that when linearizing the general two-component system a plane wave perturbation of the stationary homogeneous solution will satisfy Turing's idea can only be realized in four equivalence classes of systems characterized by the signs of the Jacobian R ′ of the reaction function. In particular, if a finite wave vector k

725-815: The properties of the underlying system is given in. In recent times, reaction–diffusion systems have attracted much interest as a prototype model for pattern formation . The above-mentioned patterns (fronts, spirals, targets, hexagons, stripes and dissipative solitons) can be found in various types of reaction–diffusion systems in spite of large discrepancies e.g. in the local reaction terms. It has also been argued that reaction–diffusion processes are an essential basis for processes connected to morphogenesis in biology and may even be related to animal coats and skin pigmentation. Other applications of reaction–diffusion equations include ecological invasions, spread of epidemics, tumour growth, dynamics of fission waves, wound healing and visual hallucinations. Another reason for

754-411: The same term [REDACTED] This disambiguation page lists articles associated with the title Kinesis . If an internal link led you here, you may wish to change the link to point directly to the intended article. Retrieved from " https://en.wikipedia.org/w/index.php?title=Kinesis&oldid=1185032495 " Category : Disambiguation pages Hidden categories: Short description

783-426: The substances are transformed into each other, and diffusion which causes the substances to spread out over a surface in space. Reaction–diffusion systems are naturally applied in chemistry . However, the system can also describe dynamical processes of non-chemical nature. Examples are found in biology , geology and physics (neutron diffusion theory) and ecology . Mathematically, reaction–diffusion systems take

812-534: Was demonstrated that kinesis is beneficial for assimilation of both patches and fluctuations of food distribution. Kinesis may delay invasion and spreading of species with the Allee effect . Reaction%E2%80%93diffusion system Reaction–diffusion systems are mathematical models that correspond to several physical phenomena. The most common is the change in space and time of the concentration of one or more chemical substances: local chemical reactions in which

841-496: Was originally used to describe the spreading of biological populations , the Newell–Whitehead-Segel equation with R ( u ) = u (1 − u ) to describe Rayleigh–Bénard convection , the more general Zeldovich–Frank-Kamenetskii equation with R ( u ) = u (1 − u )e and 0 < β < ∞ ( Zeldovich number ) that arises in combustion theory, and its particular degenerate case with R ( u ) = u − u that

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