相关论文: Limit Cycle Oscillations in Pacemaker Cells
Mathematical models for physiological processes aid qualitative understanding of the impact of various parameters on the underlying process. We analyse two such models for human physiological processes: the Mackey-Glass and the Lasota…
Rhythmic behaviors in neural systems often combine features of limit cycle dynamics (stability and periodicity) with features of near heteroclinic or near homoclinic cycle dynamics (extended dwell times in localized regions of phase space).…
By introducing a max-plus dynamical system having limit cycles, we discuss their periodicity, especially the number of discrete states in them. We also find that quasi-periodic cycles exist depending on the bifurcation parameter in the…
Multirhythmicity, a form of multistability, in an oscillator is an intriguing phenomenon found across many branches of science. From an application point of view, while the multirhythmicity is sometimes desirable as it presents us with many…
In recent decades, piecewise linear differential systems have attracted considerable attention due to their ability to describe a wide range of phenomena. A central problem, as in the theory of general planar differential systems, is to…
We consider a model system of two coupled Hopfield neurons, which is described by delay differential equations taking into account the finite signal propagation and processing times. When the delay exceeds a critical value, a limit cycle…
This paper is concerned with robust instability analysis for linear multi-agent dynamical systems with cyclic structure. This relates to interesting and important periodic oscillation phenomena in biology and neuronal science, since the…
These last years an increasing interest appeared for studying the planar discontinuous piecewise differential systems motivated by the rich applications in modelling real phenomena. One of the difficulties for understanding the dynamics of…
Nonlinear dynamics of a bouncing ball moving in gravitational field and colliding with a moving limiter is considered. Displacement of the limiter is a quadratic function of time. Several dynamical modes, such as fixed points, 2 - cycles…
Spatially distributed limited-cycle oscillators are seen in various physical and biological systems. In internal organs, mechanical motions are induced by the stimuli of spatially distributed limit-cycle oscillators. We study several…
Circadian rhythms are archetypical examples of nonlinear oscillations. While these oscillations are usually attributed to circuits of biochemical interactions among clock genes and proteins, recent experimental studies reveal that they are…
We propose a method for designing two-dimensional limit-cycle oscillators with prescribed periodic trajectories and phase response properties based on the phase reduction theory, which gives a concise description of weakly-perturbed…
It this paper we study a class of perturbed Hamiltonian systems under perturbations of thirteen order in order to detect the number of limit cycles which bifurcate from some periodic orbits of the unperturbed Hamiltonian system. The system…
We consider effect of stochastic sources upon self-organization process being initiated with creation of the limit cycle. General expressions obtained are applied to the stochastic Lorenz system to show that departure from equilibrium…
We investigate the instabilities and bifurcations of traveling pulses in a model excitable medium; in particular we discuss three different scenarios for the loss of stability resp. the disappearance of stable pulses. In numerical…
Discrete-time models are very convenient to simulate a nonlinear system on a computer. In order to build the discrete-time simulation models for the nonlinear feedback systems (which is a very important class of systems in many…
We study a class of planar continuous piecewise linear vector fields with three zones. Using the Poincar\'e map and some techniques for proving the existence of limit cycles for smooth differential systems, we prove that this class admits…
Periodicity and relaxation are investigated for the trajectories of the states in one-dimensional finite cellular automata with rule-90 and 150. The time evolutions are described with matrices. Eigenvalue analysis is applied to clarify the…
We study rate-induced phase-tipping (RP-tipping) between two stable limit cycles of a birhythmic oscillator. We say that such an oscillator RP-tips when a time variation of an input parameter preserves the bistability of the limit cycles…
Optomechanical systems are known to exhibit a rich set of complex dynamical features including various types of chaotic behavior and multi-stability. Although this exotic behavior has attracted an intense research interest, the utilization…