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A Scalar Poincaré Map for Anti-phase Bursting in Coupled Inhibitory Neurons With Synaptic Depression [PDF]
Frontiers in Applied Mathematics and Statistics, 2022 Short-term synaptic plasticity is found in many areas of the central nervous system. In the inhibitory half-center central pattern generators involved in locomotion, synaptic depression is believed to act as a burst termination mechanism, allowing ...
Mark Olenik, Conor Houghton
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Global Dynamics of a Predator–Prey Model with Fear Effect and Impulsive State Feedback Control
Mathematics, 2022 In this paper, a predator–prey model with fear effect and impulsive state control is proposed and analyzed. By constructing an appropriate Poincaré map, the dynamic properties of the system, including the existence, nonexistence, and stability of ...
Yangyang Su, Tongqian Zhang
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Bifurcation of big periodic orbits through symmetric homoclinics, application to Duffing equation [PDF]
Journal of Mahani Mathematical Research, 2023 We consider a planar symmetric vector field that undergoes a homoclinic bifurcation. In order to study the existence of exterior periodic solutions of the vector field around broken symmetric homoclinic orbits, we investigate the existence of fixed ...
Liela Soleimani, Omid RabieiMotlagh
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Poincaré Map for Discontinuous Fractional Differential Equations
Mathematics, 2022 We work with a perturbed fractional differential equation with discontinuous right-hand sides where a discontinuity function crosses a discontinuity boundary transversally.
Ivana Eliašová, Michal Fečkan
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Quasi-Periodic Oscillations of Roll System in Corrugated Rolling Mill in Resonance
Mathematics, 2021 This paper investigates quasi-periodic oscillations of roll system in corrugated rolling mill in resonance. The two-degree of freedom vertical nonlinear mathematical model of roller system is established by considering the nonlinear damping and nonlinear
Dongping He +3 more
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Discretization of Poincaré map
Electronic Journal of Qualitative Theory of Differential Equations, 2013 We analytically study the relationship between the Poincaré map and its one step discretization. Error estimates are established depending basically on the right hand side function of the investigated ODE and the given numerical scheme. Our basic tool is
Michal Fečkan, S. Kelemen
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Torus and Subharmonic Motions of a Forced Vibration System in 1 : 5 Weak Resonance
Advances in Mathematical Physics, 2020 The Neimark-Sacker bifurcation of a forced vibration system is considered in this paper. The series solution to the motion equation is obtained, and the Poincaré map is established.
Yong Guo
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Poincaré Map Approach to Global Dynamics of the Integrated Pest Management Prey-Predator Model
Complexity, 2020 An integrated pest management prey-predator model with ratio-dependent and impulsive feedback control is investigated in this paper. Firstly, we determine the Poincaré map which is defined on the phase set and discuss its main properties including ...
Zhenzhen Shi +3 more
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Complexity, 2020 The phytoplankton-fish model for catching fish with impulsive feedback control is established in this paper. Firstly, the Poincaré map for the phytoplankton-fish model is defined, and the properties of monotonicity, continuity, differentiability, and ...
Dezhao Li, Yu Liu, Huidong Cheng
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Dynamical Properties of a Herbivore-Plankton Impulsive Semidynamic System with Eating Behavior
Complexity, 2020 In this paper, an impulsive semidynamic system of the relationship between plankton and herbivore is established, and the Poincaré map method is used to extend the new properties of the model.
Yufei Wang, Huidong Cheng, Qingjian Li
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