Converging evidence in support of common dynamical principles for speech and movement coordination

1984 ◽  
Vol 246 (6) ◽  
pp. R928-R935 ◽  
Author(s):  
J. A. Kelso ◽  
B. Tuller

We suggest that a principled analysis of language and action should begin with an understanding of the rate-dependent, dynamical processes that underlie their implementation. Here we present a summary of our ongoing speech production research, which reveals some striking similarities with other work on limb movements. Four design themes emerge for articulatory systems: 1) they are functionally rather than anatomically specific in the way they work; 2) they exhibit equifinality and in doing so fall under the generic category of a dynamical system called point attractor; 3) across transformations they preserve a relationally invariant topology; and 4) this, combined with their stable cyclic nature, suggests that they can function as nonlinear, limit cycle oscillators (periodic attractors). This brief inventory of regularities, though not mean to be inclusive, hints strongly that speech and other movements share a common, dynamical mode of operation.

1987 ◽  
Vol 7 (3) ◽  
pp. 319-335
Author(s):  
Jan Barkmeijer

AbstractWe present a dynamical system in ℝ2 with a global point attractor but so that two such systems, when coupled by linear diffusion, produce a system in ℝ4 with no point attractors and yet with all solutions bounded in the positive time direction.


Author(s):  
Ayan Dutta ◽  
Debapriya Das ◽  
Dhruba Banerjee ◽  
Jayanta K. Bhattacharjee

2019 ◽  
Vol 61 (11) ◽  
pp. 112001 ◽  
Author(s):  
M Sasaki ◽  
Y Kawachi ◽  
R O Dendy ◽  
H Arakawa ◽  
N Kasuya ◽  
...  

2019 ◽  
Vol 29 (12) ◽  
pp. 1950166 ◽  
Author(s):  
Ting Yang ◽  
Qigui Yang

Intuitively, a finite-dimensional autonomous system of ordinary differential equations can only generate finitely many chaotic attractors. Amazingly, however, this paper finds a three-dimensional autonomous dynamical system that can generate infinitely many chaotic attractors. Specifically, this system can generate infinitely many coexisting chaotic attractors and infinitely many coexisting periodic attractors in the following three cases: (i) no equilibria, (ii) only infinitely many nonhyperbolic double-zero equilibria, and (iii) both infinitely many hyperbolic saddles and nonhyperbolic pure-imaginary equilibria. By analyzing the stability of double-zero and pure-imaginary equilibria, it is shown that the classic Shil’nikov criteria fail in verifying the existence of chaos in the above three cases.


2014 ◽  
Vol 136 (3) ◽  
pp. 1307-1311 ◽  
Author(s):  
Shrikanth Narayanan ◽  
Asterios Toutios ◽  
Vikram Ramanarayanan ◽  
Adam Lammert ◽  
Jangwon Kim ◽  
...  

2002 ◽  
Vol 124 (2) ◽  
pp. 327-332 ◽  
Author(s):  
Tom Bucklaew ◽  
Ching-Shi Liu

In this brief the dynamic behavior of a parametrically forced manipulator, or pendulum, system with PD control is examined. For an excitation of sufficient amplitude or frequency a Hopf bifurcation to a steady-state limit cycle is shown to result, appearing as a precursor to instability. The parameter space is mapped in order to illustrate regions where control failure will likely occur, even in the strongly damped case. For weakly damped systems, the Hopf bifurcation can additionally exhibit a dependence on initial conditions. The resulting case of competing point and periodic attractors is discussed.


2003 ◽  
pp. 253-272 ◽  
Author(s):  
Antje S. Meyer ◽  
Christian Dobel

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