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homeostasis given in Eqs. (11a), (11b) and (11c). Moreover, since other systems, such as social

Figure 3. Pseudo-random behavior of the system with latent time of "decision making". Circle designates an initial state

Solutions of the dynamical equations of homeostasis show that there are four types of system behavior. In the first, the system generates activity that quickly takes it to the main ground state with zero damage and stress (Figure 1A). In the second, the main ground state cannot be achieved; however, the system finds another ground state without damage and stress as well (Figure 1B). In the third, homeostasis cannot find the state with zero damage and stress and the system arrives at the damaged and distressed, but stable stationary states (Figure 1C). In the last type of behavior, the system cannot achieve any stable state, level of stress dramatically increases, system variables leave the life-compatible region, and the system moves toward death (Figure 2). It should be noted that there is a critical value of injure, which leads to fatal instability of a system by violation of the condition (21). Apparently, there is a critical value of the stress as well, so if S-index exceeds this value, an organism inevitably moves toward death. Note that near the injured stable states, where Iðxc;ScÞ > 0, the critical value of the stress may be lower than near uninjured states,<sup>18</sup> that is, injured organism is more sensitive to the stress

All types of behavior are described by the same system of Eqs. (11b) and (11c) and S-Lagrangian, but differ by initial and/or environmental conditions (which are described by parameters of the Lagrangian). It was found that systems exhibiting homeostasis may have at least two types of variables. The first type is C-variables, which have stationary values in the stable states of the system. Injury disturbs these values and excites protection mechanisms. The other types

<sup>∂</sup>S� <sup>J</sup><sup>−</sup> <sup>Φ</sup>2ðS�Þþð <sup>S</sup>� <sup>∂</sup>Φ<sup>2</sup>

∂S� ÞΓ ¼ 0.

For <sup>I</sup>ðx;S<sup>Þ</sup> and <sup>A</sup>ðx;S<sup>Þ</sup> from Eqs. (29a) and (29b), the critical value of S-index is obtained from <sup>∂</sup>Φ<sup>1</sup>

systems, may also possess distress or discomfort, they may also undergo homeostasis.

than the healthy one.

18

and Star designates the finish state.

162 Lagrangian Mechanics

