相关论文: New dynamics in cerebellar Purkinje cells: torus c…
In the first half of the paper, some recent advances in coupled dynamical systems, in particular, a globally coupled map are surveyed. First, dominance of Milnor attractors in partially ordered phase is demonstrated. Second, chaotic…
In order to remain adaptable to a dynamic environment, neural activity must be simultaneously both sensitive and stable. To solve this problem, the brain has been hypothesised to sit near a critical boundary. Yet, precisely how criticality…
Slow-fast systems on the two-torus are studied. As it was shown before, canard cycles are generic in such systems, which is in drastic contrast with the planar case. It is known that if the rotation number of the Poincare map is integer and…
We consider double canard cycles including two canards in singularly perturbed planar systems with two canard points. Previous work studied the complex oscillations including relaxation oscillations and canard cycles in singularly perturbed…
Dynamical properties of limit cycles in a tropically discretized negative feedback model are numerically investigated. This model has a controlling parameter $\tau$, which corresponds to time interval for the time evolution of phase in the…
Intensive computational and theoretical work has led to the development of mutliple mathematical models for bursting in respiratory neurons in the pre-B\"otzinger Complex (pre-B\"otC) of the mammalian brainstem. Nonetheless, these previous…
Critical transitions describe sudden changes in the state of an ecosystem. In classical bifurcation theory, such transitions occur when the value of a parameter exceeds a threshold (``bifurcation") value. More recently, critical transitions…
A generic saddle-node bifurcation is proposed to modelize fast transitions of finite amplitude arising in geophysical (and perhaps other) contexts, when they result from the intrinsic dynamics of the system. The fast transition is…
A new four-dimensional model with quasi-periodic dynamics is suggested. The torus attractor originates via the saddle-node bifurcation, which may be regarded as a member of a bifurcation family embracing different types of blue sky…
Transition to turbulence dramatically alters the properties of fluid flows. In most canonical shear flows, the laminar flow is linearly stable and a finite-amplitude perturbation is necessary to trigger transition. Controlling transition to…
Nonlinear dynamical systems may be exposed to tipping points, critical thresholds at which small changes in the external inputs or in the systems parameters abruptly shift the system to an alternative state with a contrasting dynamical…
The behavior of a dynamical system can exhibit abrupt changes when it crosses a tipping point. To prevent catastrophic events, it is useful to analyze indicators of the incoming bifurcation, as the divergence of the relaxation time of the…
The canard explosion is the change of amplitude and period of a limit cycle born in a Hopf bifurcation in a very narrow parameter interval. The phenomenon is well understood in singular perturbation problems where a small parameter controls…
Self-sustained subthreshold oscillations in a discrete-time model of neuronal behavior are considered. We discuss bifurcation scenarios explaining the birth of these oscillations and their transformation into tonic spikes. Specific features…
The results of a combined experimental and numerical study of the flow in slowly diverging pipes are presented. Interestingly, an axisymmetric conical recirculation cell has been observed. The conditions for its existence and the length of…
We present new experimental results on the quenching dynamics of an extended thermo-convective system (a network array of approximately 100 convective oscillators) going through a secondary subcritical bifurcation. We characterize a…
The May--Leonard model was introduced to examine the behavior of three competing populations where rich dynamics, such as limit cycles and nonperiodic cyclic solutions, arise. In this work, we perturb the system by adding the capability of…
For the reduced two-dimensional Belousov-Zhabotinsky slow-fast differential system, the known results are the existence of one limit cycle and its stability for particular values of the parameters. Here, we characterize all dynamics of this…
Canards are special solutions to ordinary differential equations that follow invariant repelling slow manifolds for long time intervals. In realistic biophysical single cell models, canards are responsible for several complex neural rhythms…
Bursting is a periodic transition between a quiescent state and a state of repetitive spiking. The phenomenon is ubiquitous in a variety of neurophysical systems. We numerically study the dynamical properties of a normal form of subcritical…