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Neimark–Sacker Bifurcations in Planar, Piecewise-Smooth, Continuous Maps [PDF]
SIAM Journal on Applied Dynamical Systems, 2008 The multipliers of a fixed point of a piecewise-smooth, continuous map may change discontinuously as the fixed point crosses a discontinuity under smooth variation of parameters. We study the case when the multipliers “jump” from inside to outside the unit circle, and we assume the map is two-dimensional and piecewise-affine.
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Mathematical and Computer Modelling of Dynamical SystemsIn this paper, a discrete predator-prey model incorporating herd behaviour and square root response function is deduced from its continuous version by the semi-discretization method.
Danyang Li, Xianyi Li
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Stability and Bifurcation of a Class of Discrete-Time Cohen-Grossberg Neural Networks with Delays
Discrete Dynamics in Nature and Society, 2011 A class of discrete-time Cohen-Grossberg neural networks with delays is investigated in this paper. By analyzing the corresponding characteristic equations, the asymptotical stability of the null solution and the existence of Neimark-Sacker bifurcations ...
Qiming Liu, Rui Xu, Zhiping Wang
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MathematicsIn this paper, we use a semi-discretization method to consider the predator–prey model of Leslie type with ratio-dependent simplified Holling type IV functional response.
Luyao Lv, Xianyi Li
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A study of resonance tongues near a Chenciner bifurcation using MatcontM [PDF]
, 2011 MatcontM is a matlab toolbox for numerical analysis of bifurcations of fixed points and periodic orbits of maps. It computes codim 1 bifurcation curves and supports the computation of normal coefficients including branch switching from codim 2 points to ...
Govaerts, W. +3 more
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Controlling Neimark-Sacker Bifurcation in Delayed Species Model Using Feedback Controller
Advances in Mathematical Physics, 2016 Based on the stability and orthogonal polynomial approximation theory, the ordinary, dislocated, enhancing, and random feedback control methods are used to suppress the Neimark-Sacker bifurcation to fixed point in this paper. It is shown that the convergence rate of enhancing feedback control and random feedback control can be faster than those of ...
Jie Ran, Yanmin Liu, Jun He, Xiang Li
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Open Mathematics, 2022 In this paper, a discrete Leslie-Gower predator-prey system with Michaelis-Menten type harvesting is studied. Conditions on the existence and stability of fixed points are obtained.
Chen Jialin +3 more
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Stability and Cycles in a Cobweb Model with Heterogeneous Expectations [PDF]
We investigate the dynamics of a cobweb model with heterogeneous beliefs, generalizing the example of Brock and Hommes (1997). We examine situations where the agents form expectations by using either rational expectations, or a type of adaptive ...
Clem Tisdell +2 more
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Bifurcations and chaos in a novel discrete economic system
Advances in Mechanical Engineering, 2019 In this article, a novel discrete system based on an economic model is introduced. Conditions for local stability of the model’s fixed points are obtained. Existence of supercritical Neimark–Sacker bifurcation is shown around the game’s Nash equilibrium.
A Al-khedhairi, AE Matouk, SS Askar
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IEEE Access, 2020 Vegetation pattern is one of the most important self-organized patterns in ecological systems. The formation mechanism of vegetation patterns has been attributed to dynamic bifurcations, while from the external perspective, the regularity of patterns ...
Feifan Zhang +4 more
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