TC-HAT

TC-HAT: a novel toolbox for the continuation of periodic trajectories in hybrid dynamical systems. This paper describes the underlying formulation and functionality of the newly developed software program TC-HAT, to perform bifurcation analysis of systems in which continuous-in-time dynamics are interrupted by discrete-in-time events, often referred to as hybrid dynamical systems. Boundary-value-problem formulations corresponding to single- and two-parameter continuations of periodic trajectories and selected associated codimension-one bifurcations in such systems are presented. Finally, the capabilities of the program are illustrated by performing bifurcation analysis of a few example hybrid dynamical systems.


References in zbMATH (referenced in 11 articles , 1 standard article )

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  1. Han, Ning; Cao, Qingjie; Liang, Tingwei: A rotating disk linked by a pair of springs (2015)
  2. Xu, Jieqiong; Chen, Pu; Li, Qunhong: Theoretical analysis of co-dimension-two grazing bifurcations in $n$-degree-of-freedom impact oscillator with symmetrical constrains (2015)
  3. Páez Chávez, Joseph; Wiercigroch, Marian: Bifurcation analysis of periodic orbits of a non-smooth Jeffcott rotor model (2013)
  4. Křivan, Vlastimil: On the Gause predator-prey model with a refuge: a fresh look at the history (2011)
  5. Colombo, Alessandro; Dercole, Fabio: Discontinuity induced bifurcations of nonhyperbolic cycles in nonsmooth systems (2010)
  6. Barton, David A.W.: Stability calculations for piecewise-smooth delay equations (2009)
  7. Colombo, A.; Galvanetto, U.: Stable manifolds of saddles in piecewise smooth systems (2009)
  8. Colombo, Alessandro; Lamiani, Paola; Benadero, Luis; di Bernardo, Mario: Two-parameter bifurcation analysis of the buck converter (2009)
  9. Kalmár-Nagy, Tamás; Shekhawat, Ashivni: Nonlinear dynamics of oscillators with bilinear hysteresis and sinusoidal excitation (2009)
  10. Nordmark, Arne; Dankowicz, Harry; Champneys, Alan: Discontinuity-induced bifurcations in systems with impacts and friction: discontinuities in the impact law (2009)
  11. Thota, Phanikrishna; Dankowicz, Harry: TC-HAT ($\widehatTC$): a novel toolbox for the continuation of periodic trajectories in hybrid dynamical systems (2008)