Related papers: Periodicity of limit cycles in a max-plus dynamica…
Dynamical properties of a generalized max-plus model for ultradiscrete limit cycles are investigated.This model includes both the negative feedback model and the Sel'kov model. It exhibits the Neimark-Sacker bifurcation, and possesses…
In this paper we complete the global qualitative analysis of a quartic ecological model. In particular, studying global bifurcations of singular points and limit cycles, we prove that the corresponding dynamical system has at most two limit…
Linear max-plus systems describe the behavior of a large variety of complex systems. It is known that these systems show a periodic behavior after an initial transient phase. Assessment of the length of this transient phase provides…
The main objective of this paper is to study the number of limit cycles in a family of polynomial systems. Using bifurcation methods, we obtain the maximal number of limit cycles in global bifurcation.
Stability and bifurcation properties of one-dimensional discrete dynamical systems with positivity, which are derived from continuous ones by tropical discretization, are studied. The discretized time interval is introduced as a bifurcation…
In order to investigate the evolutionary process of many deterministic Dynamical systems with unfixed parameter, a set of dynamical models with parameter changing continuously and the accumulation of this change might be large is introduced…
Planar piecewise linear systems with two linearity zones separated by a straight line and with a periodic orbit at infinity are considered. By using some changes of variables and parameters, a reduced canonical form with five parameters is…
Dynamical properties of tropically discretized and max-plus negative feedback models are investigated. Reviewing the previous study [S. Gibo and H. Ito, J. Theor. Biol. 378, 89 (2015)], the conditions under which the Neimark-Sacker…
In this paper, we consider a planar dynamical system with a piecewise linear function containing an arbitrary number (but finite) of dropping sections and approximating some continuous nonlinear function. Studying all possible local and…
In this paper, we carry out a global qualitative analysis of a reduced planar quartic Topp system which models the dynamics of diabetes. In particular, studying global bifurcations, we prove that such a system can have at most two limit…
In this paper, we study the problem of limit cycle bifurcation in two piecewise polynomial systems of Li\'enard type with multiple parameters. Based on the developed Melnikov function theory, we obtain the maximum number of limit cycles of…
We investigate the dynamical properties of cusp bifurcations in max-plus dynamical systems derived from continuous differential equations through the tropical discretization and the ultradiscrete limit. A general relationship between cusp…
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…
Max-plus equations are derived from tropically discretized Sel'kov model via ultradiscretization. These max-plus equations possess common dynamical structures with the discretized model: Neimark-Sacker bifurcation and limit cycles. The…
Limit cycles are self-sustained, closed trajectories in phase space representing (un)-stable, periodic behavior in nonlinear dynamical systems. They underpin diverse natural phenomena, from neuronal firing patterns to engineering…
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…
In this paper, we consider sufficient conditions for an invariant double circle to occur in a one parameter discrete dynamical systems on a cylinder.
The present paper is devoted to the study of the maximum number of limit cycles bifurcated from the periodic orbits of the quadratic isochronous center $\dot{x}=-y+\frac{16}{3}x^{2}-\frac{4}{3}y^{2},\dot{y}=x+\frac{8}{3}xy$ by the averaging…
In this paper, an interesting and new bifurcation phenomenon that limit cycles could be bifurcated from nilpotent node (focus) by changing its stability was investigated. It is different from lowing its multiplicity in order to get limit…
We approximate a chain recurrent dynamical system by periodic dynamical systems. This is similar to the well known Bohr theorem on approximation of almost periodic functions by periodic functions.