Related papers: Switching between oscillations and homeostasis in …
We study the versatile performance of networks of coupled circuits. Each of these circuits is composed of a positive and a negative feedback loop in a motif that is frequently found in genetic and neural networks. When two of these circuits…
Differential equation-based physiological models of sleep-wake networks describe sleep-wake regulation by simulating the activity of wake- and sleep-promoting neuronal populations and the modulation of these populations by homeostatic and…
Autonomous sustained oscillations are ubiquitous in living and nonliving systems. As open systems, far from thermodynamic equilibrium, they defy entropic laws which mandate convergence to stationarity. We present structural conditions on…
Oscillatory dynamics are ubiquitous in biological networks. Possible sources of oscillations are well understood in low-dimensional systems, but have not been fully explored in high-dimensional networks. Here we study large networks…
Homeostasis is a running theme in biology. Often achieved through feedback regulation strategies, homeostasis allows living cells to control their internal environment as a means for surviving changing and unfavourable environments. While…
Organisms are equipped with regulatory systems that display a variety of dynamical behaviours ranging from simple stable steady states, to switching and multistability, to oscillations. Earlier work has shown that oscillations in protein…
We report a noise induced delay of bifurcation in a simple pulse-coupled neural circuit. We study the behavior of two neural oscillators, each individually governed by saddle-node dynamics, with reciprocal excitatory synaptic connections.…
Oscillatory systems with time-delayed pulsatile feedback appear in various applied and theoretical research areas, and received a growing interest in the last years. For such systems, we report a remarkable scenario of destabilization of a…
We disclose the generality of the intrinsic mechanisms underlying multistability in reciprocally inhibitory 3-cell circuits composed of simplified, low-dimensional models of oscillatory neurons, as opposed to those of a detailed Hodgkin-…
We study the problem of controlling oscillations in closed loop by combining positive and negative feedback in a mixed configuration. We develop a complete design procedure to set the relative strength of the two feedback loops to achieve…
Using a stochastic nonlinear phase oscillator model, we study the effect of event-triggered feedback on the statistics of interevent intervals. Events are associated with the entering of a new cycle. The feedback is modeled by an…
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.…
The Kuramoto model is a standard model for the dynamics of coupled oscillator networks. In particular, it is used to study long time behavior such as phase-locking where all oscillators rotate at a common frequency with fixed angle…
Following the long-lived qualitative-dynamics tradition of explaining behavior in complex systems via the architecture of their attractors and basins, we investigate the patterns of switching between qualitatively distinct trajectories in a…
The theory of mixed-feedback systems provides an effective framework for the design of robust and tunable oscillations in nonlinear systems characterized by interleaved fast positive and slow negative feedback loops. The goal of this paper…
Oscillation has an important role in bio-dynamical systems such as circadian rhythms and eukaryotic cell cycle. John Tyson et. al. in Nature Review Mol Cell Biol 2008 examined a limited number of network topologies consisting of three nodes…
We study the oscillatory behaviour of a gene regulatory network with interlinked positive and negative feedback loop. Frequency and amplitude are two important properties of oscillation. Studied network produces two different modes of…
It is well known that the addition of noise to a multistable dynamical system can induce random transitions from one stable state to another. For low noise, the times between transitions have an exponential tail and Kramers' formula gives…
This paper presents a stability analysis of simple neuromodules displaying fold bifurcations (leading to hysteresis), flip bifurcations (period doubling and undoubling to and from chaos) and Neimark-Sacker bifurcations (quasiperiodic and…
The coexistence of an abnormal rhythm and a normal steady state is often observed in nature (e.g., epilepsy). Such a system is modeled as a bistable oscillator that possesses both a limit cycle and a fixed point. Although bistable…