Bursting multistability induced by double-Hopf bifurcation
نویسندگان
چکیده
We study the slow–fast dynamics of a system with double-Hopf bifurcation and slowly varying parameter. The model consists coupled Bonhöffer–van der Pol oscillators excited by periodic slow-varying AC source. consider two cases where parameter passes or crosses bifurcation, respectively. Due to system’s multistability, bursting solutions are observed in each case: single-mode two-mode bursting. Further investigation reveals that causes stable coexistence these solutions. mechanism such is explained using changing phase portraits fast subsystem. also show robustness effect vicinity bifurcation.
منابع مشابه
Hopf bifurcation and multistability in a system of phase oscillators.
We study the phase reduction of two coupled van der Pol oscillators with asymmetric repulsive coupling under an external harmonic force. We show that the system of two phase oscillators undergoes a Hopf bifurcation and possesses multistability on a 2π-periodic phase plane. We describe the bifurcation mechanisms of formation of multistability in the phase-reduced system and show that the Androno...
متن کاملDouble Singularity-induced Bifurcation Points and Singular Hopf Bifurcations
We explore the singularity-induced bifurcation and singular Hopf bifurcation theorems and the degeneracies that arise when Newton’s Laws are coupled to Kirchhoff’s Laws. Such models are used in the electrical engineering literature to describe electrical power systems and they can take the form of either an index-1 differential-algebraic equation (DAE) or a singularly perturbed ordinary differe...
متن کاملDelay-Induced Multistability Near a Global bifurcation
We study the effect of a time-delayed feedback within a generic model for a saddle-node bifurcation on a limit cycle. Without delay the only attractor below this global bifurcation is a stable node. Delay renders the phase space infinite-dimensional and creates multistability of periodic orbits and the fixed point. Homoclinic bifurcations, period-doubling and saddle-node bifurcations of limit c...
متن کاملDouble Hopf Bifurcation with Huygens Symmetry
Double Hopf bifurcations have been studied prior to this work in the generic nonresonant case and in certain strongly resonant cases, including 1:1 resonance. In this paper, the case of symmetrically coupled identical oscillators, motivated by the classic problem of synchronization of Huygens’ clocks, is studied using the codimension-three Elphick–Huygens equivariant normal form presented here....
متن کاملHOPF BIFURCATION CONTROL WITH PD CONTROLLER
In this paper, we investigate the problem of bifurcation control for a delayed logistic growth model. By choosing the timedelay as the bifurcation parameter, we present a Proportional - Derivative (PD) Controller to control Hopf bifurcation. We show that the onset of Hopf bifurcation can be delayed or advanced via a PD Controller by setting proper controlling parameter. Under consideration mode...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Chaos
سال: 2023
ISSN: ['1527-2443', '1089-7682', '1054-1500']
DOI: https://doi.org/10.1063/5.0157718