Titlebook: Catastrophe Theory; Vladimir Igorevich Arnold Book 19862nd edition Springer-Verlag Berlin Heidelberg 1986 Bifurcations.Catastrophe Theory.

heterogeneous

https://doi.org/10.1007/978-3-031-47880-2Let us consider an equilibrium state of a system depending on several parameters and let us assume that (in some domain of variation of the parameters) this equilibrium state does not bifurcate.

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https://doi.org/10.1007/978-3-031-48777-4A . in phase space is defined as follows: at every point of the space we have not just one velocity vector (as in the usual evolutionary system), but a whole set of vectors called the . (Fig. 49).

Cytokines

ATRIA

多嘴多舌

bromide

A Catastrophe Machine,In contrast to the example given above, the application of singularity theory to the study of bifurcations of equilibrium states in the theory of elasticity is irreproachably founded.

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Bifurcations of Equilibrium States,An . is described mathematically by a vector field in phase space. A point of phase space defines the . of the system. The vector at this point indicates the velocity of change of the state.

Eeg332

滔滔不绝地说

Singularities of the Boundary of Attainability,A . in phase space is defined as follows: at every point of the space we have not just one velocity vector (as in the usual evolutionary system), but a whole set of vectors called the . (Fig. 49).

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