相关论文: Wild oscillations in a nonlinear neuron model with…

Mixed-mode oscillations (MMOs) are complex oscillatory patterns in which large-amplitude relaxation oscillations (LAOs) alternate with small-amplitude oscillations (SAOs). MMOs are found in singularly perturbed systems of ordinary…

In this paper, we focus on the emergence of diverse neuronal oscillations arising in a mixed population of neurons with different excitability properties. These properties produce mixed mode oscillations (MMOs) characterized by the…

In a series of two papers, we investigate the mechanisms by which complex oscillations are generated in a class of nonlinear dynamical systems with resets modeling the voltage and adaptation of neurons. This first paper presents…

Alternating patterns of small and large amplitude oscillations occur in a wide variety of physical, chemical, biological and engineering systems. These mixed-mode oscillations (MMOs) are often found in systems with multiple time scales.…

Many neuronal systems and models display a certain class of mixed mode oscillations (MMOs) consisting of periods of small amplitude oscillations interspersed with spikes. Various models with different underlying mechanisms have been…

Mixed mode oscillations (MMOs) are complex oscillatory behaviors of multiple-timescale dynamical systems in which there is an alternation of large-amplitude and small-amplitude oscillations. It is well known that MMOs in two-timescale…

We study a class of multi-parameter three-dimensional systems of ordinary differential equations that exhibit dynamics on three distinct timescales. We apply geometric singular perturbation theory to explore the dependence of the geometry…

Mutual inhibition is a common motif in neural systems. Here, we establish that cusped singularities - folded singularities located at cusp points of critical manifolds - provide a universal organizing mechanism for mixed-mode oscillations…

Much work has been done on relaxation oscillations and other simple oscillators in conceptual climate models. However, the oscillatory patterns in climate data are often more complicated than what can be described by such mechanisms. This…

Bursting oscillations are commonly seen as a mechanism for information coding in neuroscience and have also been observed in many physical, biochemical, and chemical systems. This study focuses on the computational investigation of…

We derive rigorous results describing the asymptotic dynamics of a discrete time model of spiking neurons introduced in \cite{BMS}. Using symbolic dynamic techniques we show how the dynamics of membrane potential has a one to one…

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…

Very strong El Ni\~no events occur sporadically every 10-20 years. The origin of this bursting behavior still remains elusive. Using a simplified 3-dimensional dynamical model of the tropical Pacific climate system, which captures the El…

Chaos provides many interesting properties that can be used to achieve computational tasks. Such properties are sensitivity to initial conditions, space filling, control and synchronization. Chaotic neural models have been devised to…

We present a design framework to induce stable oscillations through mixed feedback control. We provide conditions on the feedback gain and on the balance between positive and negative feedback contributions to guarantee robust oscillations.…

We investigate the physical origin of nonlinear damping due to mode coupling between several auto-oscillatory modes driven by spin-orbit torque in constricted Py/Pt heterostructures by examining the dependence of auto-oscillation on…

We consider an ecological model consisting of two species of predators competing for their common prey with explicit interference competition. With a proper rescaling, the model is portrayed as a singularly perturbed system with one-fast…

Low-dimensional yet rich dynamics often emerge in the brain. Examples include oscillations and chaotic dynamics during sleep, epilepsy, and voluntary movement. However, a general mechanism for the emergence of low dimensional dynamics…

In this paper, we use geometric singular perturbation theory and blowup, as our main technical tool, to study the mixed-mode oscillations (MMOs) that occur in two coupled FitzHugh-Nagumo units with symmetric and repulsive coupling. In…

A detailed study of the slow manifold of a model exhibiting mixed-mode oscillations is presented. A scenario for the emergence of mixed-mode states which does not involve phase locking on a 2-torus is constructed. We show that mixed-modes…