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Analysis of a model for antagonistic muscles. (English) Zbl 0519.92011


MSC:

92Cxx Physiological, cellular and medical topics
74A20 Theory of constitutive functions in solid mechanics
74L15 Biomechanical solid mechanics
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[1] Bawa, P., Mannard, A., Stein, R.B.: Effects of elastic loads on the contractions of cat soleus muscle. Biol. Cybern.22, 129–137 (1976)
[2] Hatze, H.: A myocybernetic model of skeletal muscle. Biol. Cybern.25, 103–119 (1977) · Zbl 0346.92011
[3] Hatze, H.: Optimal processes of neuro-muskulo-skeletal control systems. In: Mathematical modelling in biomathematics. Lecture Notes in Biomathematics, Vol. 33, pp. 19–39. Berlin, Heielberg, New York: Springer 1980 · Zbl 0422.92009
[4] Hill, A.V.: The heat of shortening and the dynamic constants of muscle. Proc. R. Soc. (London) B126, 136–195 (1938)
[5] Huxley, A.F., Simmons, R.M.: Proposed mechanism of forece generation in striated muscle. Nature (London)233, 533–538 (1971)
[6] Margaria, R.: Biomechanics and energetics of muscular exercise. Oxford: Clarendon Press 1976
[7] Oğuztöreli, M.N., Stein, R.B.: An analysis of oscillations in neuromuscular systems. J. Math. Biol.2, 87–105 (1975) · Zbl 0309.92007
[8] Oğuztöreli, M.N., Stein, R.B.: The effects of multiple reflex pathways on the oscillations in neuro-muscular systems. J. Math. Biol.3, 87–101 (1976) · Zbl 0329.92003
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[10] Oğuztöreli, M.N., Stein, R.B.: Neuromuscular resetting and entrainment. Appl. Math. Comp.7, 93–124 (1980) · Zbl 0439.92007
[11] Parmiggiani, F., Stein, R.B.: Nonlinear summation of contrations in cat muscles. II. The later facilitation and stiffness changes. J. Gen. Physiol.78, 295–311 (1981)
[12] Parmiggiani, F., Stein, R.B., Rolf, R.: Slow changes and Wiener analysis of nonlinear summation in contractions of cat muscles. Biol. Cybern.42, 177–188 (1981)
[13] Stein, R.B., Oğuztöreli, M.N.: Tremor and other oscillations in neuro-muscular systems. Biol. Cybern.22, 147–157 (1976) · Zbl 0321.92008
[14] Stein, R.B., Oğuztöreli, M.N.: Reflex involvement in the generation and control of tremor and clonus. In: Physiological tremor, pathological tremors, and clonus. Desmedt, J.E. (ed.). Prog. Clin. Neurophysiol.5, 28–50 (1978)
[15] Stein, R.B., Oğuztöreli, M.N.: The role of {\(\gamma\)}-motoneurons in mammalian reflex systems. Biol. Cybern.39, 171–179 (1981) · Zbl 0457.92005
[16] Stein, R.B., Oğuztöreli, M.N.: A model of whole muscles incorporating functionally important nonlinearities. In: Nonlinear phenomena in mathematical sciences. Lakshimikantham, V. (ed.). New York: Academic Press 1982 (in press)
[17] Stein, R.B., Parmiggiani, F.: Nonlinear summation of contractions in cat muscles. I. The early depression. J. Gen. Physiol.78, 295–311 (1981)
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