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Dynamical systems can be designed to exhibit a range of distinct behaviors, which all arise from the same set of continuous dynamics when the latter bifurcates, triggered by a switch in one of its scalar parameters. Building on recent advances that introduce motivation and value dynamics as an efficient way to design multi-behavioral systems, this paper lifts some of the existing restrictions on what kind of planar vector fields can be combined to produce bifurcations. This relaxation enriches the class of dynamical systems that such an approach applies, and gives rise to new behaviors. The paper identifies new analytical conditions under which this new set of planar vector fields can undergo Hopf bifurcations and result in a multi-behavioral system. Numerical simulations and experimental results confirm the theoretical predictions for the existence of the Hopf bifurcations and the applicability of the theory in real systems.
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Constructing continuous multi-behavioral planar systems through motivation dynamics and bifurcations
This paper offers new analytical conditions on the system parameters of a particular class of planar dynamical systems which would allow them to undergo a Hopf bifurcation. These systems are constructed as a means of generating multiple behaviors from the same single continuous dynamical system model, without resorting to switching between distinct component continuous dynamics associated to each behavioral mode. This work builds on recent advances which introduced motivation dynamics as an efficient way to design multi-behavioral systems. The contribution of this paper is that it expands the scope of the motivation dynamics approach, and offers explicit analytic conditions on the system parameters to guarantee the existence of bifurcations, which can then be utilized to better engineer the structure and location of the resulting equilibria. Numerical simulations confirm the theoretical predictions for the onset of the Hopf bifurcations.
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- Award ID(s):
- 2014264
- PAR ID:
- 10366176
- Date Published:
- Journal Name:
- 60th IEEE Conference on Decision and Control
- Page Range / eLocation ID:
- 1095 to 1100
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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- Free Publicly Accessible Full Text
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Accepted Manuscript1.0
- Conference Paper:
- https://doi.org/10.1109/CDC45484.2021.9683759
