A simple integrate-and-fire system and various super-stable periodic orbits

被引：4
|
作者：
Takahashi, Risa [1 ]
Saito, Toshimichi [1 ]
机构：
[1] Hosei Univ, EE Dept, Koganei, Tokyo 184, Japan
来源：
IEICE NONLINEAR THEORY AND ITS APPLICATIONS | 2018年 / 9卷 / 01期
关键词：
switched dynamical systems; super-stable periodic orbits; chaos;
D O I：
10.1587/nolta.9.11
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
This paper studies super-stable periodic orbits and related phenomena in a simple switched dynamical system. The system repeats integrate-and-fire behavior between a constant threshold and a periodic base signal. The base signal consists of two components: the fundamental and higher frequency triangular signals. First, we demonstrate "chaos + chaos = order" such that the system exhibits chaos if the base signal is either of the two components whereas the system exhibits a super-stable periodic orbit if the base signal consists of both components. This phenomenon is confirmed experimentally and is explained theoretically. Second, we extract two key parameters and show that the system can exhibit a variety of super-stable periodic orbits. Applying a mapping procedure, existence regions of basic super-stable periodic orbits are calculated precisely.
引用
收藏
页码：11 / 23
页数：13
相关论文
共 50 条
  • [31] Asymptotically stable periodic orbits of a coupled electromechanical system
    Dantas, M. J. H.
    Sampaio, R.
    Lima, R.
    NONLINEAR DYNAMICS, 2014, 78 (01) : 29 - 35
  • [32] Time-scale matching in the response of a leaky integrate-and-fire neuron model to periodic stimulus with additive noise
    Shimokawa, T
    Pakdaman, K
    Sato, S
    PHYSICAL REVIEW E, 1999, 59 (03): : 3427 - 3443
  • [33] Periodic orbits in a simple ray-splitting system
    Biswas, D
    PHYSICAL REVIEW E, 1996, 54 (02): : 1232 - 1236
  • [34] Synchronization of the neural response to noisy periodic synaptic input in a balanced leaky integrate-and-fire neuron with reversal potentials
    Burkitt, AN
    IJCNN'01: INTERNATIONAL JOINT CONFERENCE ON NEURAL NETWORKS, VOLS 1-4, PROCEEDINGS, 2001, : 22 - 27
  • [35] Analysis of Various Periodic Orbits in Simple Dynamic Binary Neural Networks
    Sato, Ryuji
    Makita, Kazuma
    Saito, Toshimichi
    2016 INTERNATIONAL JOINT CONFERENCE ON NEURAL NETWORKS (IJCNN), 2016, : 2031 - 2038
  • [36] An integrate-and-fire model for pulsatility in the neuroendocrine system<?A3B2 show [editpick]?>
    Churilov, Alexander N.
    Milton, John
    Salakhova, Elvira R.
    CHAOS, 2020, 30 (08)
  • [37] Predicting neuronal activity with simple models of the threshold type:: Adaptive Exponential Integrate-and-Fire model with two compartments
    Clopath, Claudia
    Jolivet, Renaud
    Rauch, Alexander
    Luescher, Hans-Rudolf
    Gerstner, Wulfram
    NEUROCOMPUTING, 2007, 70 (10-12) : 1668 - 1673
  • [38] Chaotic phenomenon in both an integrate-and-fire circuit with periodic pulse-train input and a discrete neural network model
    Ruan, J
    Cai, ZJ
    Gu, FJ
    Xu, SX
    Lin, W
    PROCEEDING OF THE 2002 INTERNATIONAL JOINT CONFERENCE ON NEURAL NETWORKS, VOLS 1-3, 2002, : 761 - 766
  • [39] A simple feedback control system: Bifurcations of periodic orbits and chaos
    Yagasaki, K
    NONLINEAR DYNAMICS, 1996, 9 (04) : 391 - 417
  • [40] Simple feedback control system: bifurcations of periodic orbits and chaos
    Gifu Univ, Gifu, Japan
    Nonlinear Dyn, 4 (391-417):
12345