On the occurrence of bursting oscillations in the damping Helmholtz–Rayleigh–Duffing oscillator with slow-changing parametrical and external forcings DOI
Chun Zhang,

Qiaoxia Tang

Physica Scripta, Journal Year: 2023, Volume and Issue: 99(1), P. 015204 - 015204

Published: Dec. 6, 2023

Abstract Multiple timescale effects can be reflected bursting oscillations in many classical nonlinear oscillators. In this work, we are concerned about the induced by two damped Helmholtz-Rayleigh-Duffing oscillator (written as DHRDO for short) excited slow-changing parametrical and external forcings. By using trigonometric function variation authenticating slow excitations a slowly varying state variable, time-varying rewritten new time-invariant system. Then, critical conditions of some typical bifurcations presented bifurcation theory. With help analyses, six patterns, i.e., ‘Hopf/Hopf-Hopf/Hopf’ bursting, ‘fold/Homoclinic-Hopf/Hopf’ ‘fold/Homoclinic/Hopf’ ‘Hopf/fold/Homoclinic/Hopf’ ‘Hopf/Homoclinic/Homoclinic/Hopf’ ‘Hopf/Homoclinic/Hopf-Hopf/Homoclinic/Hopf’ explored slow/fast decomposition method other techniques. Our findings provide different forms oscillation modes well patterns. addition, use numerical simulation to prove correctness theoretical analyses.

Language: Английский

Periodic bursting oscillations in a hybrid Rayleigh–Van der Pol–Duffing oscillator DOI
Feng Zhao, Xindong Ma,

Shuqian Cao

et al.

Nonlinear Dynamics, Journal Year: 2022, Volume and Issue: 111(3), P. 2263 - 2279

Published: Oct. 10, 2022

Language: Английский

Citations

18
Research on multi-valued response and bursting oscillation of series multi-stable piezoelectric energy harvester DOI
Youhua Qian, Yani Chen

The European Physical Journal Plus, Journal Year: 2022, Volume and Issue: 137(5)

Published: May 1, 2022

Language: Английский

Citations

13
Control of Network Bursting in a Model Spiking Network Supplied with Memristor—Implemented Plasticity DOI Creative Commons
Sergey V. Stasenko, A. N. Mikhaylov, Victor Kazantsev

et al.

Mathematics, Journal Year: 2023, Volume and Issue: 11(18), P. 3888 - 3888

Published: Sept. 12, 2023

We consider an unstructured neuron network model composed of excitatory and inhibitory neurons. The synaptic connections are supplied with spike timing-dependent plasticity (STDP). take the STDP implemented using a memristor. In normal conditions, forms so-called bursting discharges typical living networks in dissociated neuronal cultures. Incorporating biologically inspired model, we demonstrate how memristive emulates plasticity, which is crucial for regulating synchronous brain activity. have found that, when memristor-based activated, dynamics suppressed turns to random spiking mode. dependence properties on degree analyzed. These findings hold implications advancing invasive neurointerfaces identification management epileptiform

Language: Английский

Citations

6
Experimental observation of distinct amplitude-modulated bursting in Liénard system DOI Creative Commons
S. Leo Kingston,

S. Dinesh Vijay,

Suresh Kumarasamy

et al.

The European Physical Journal Plus, Journal Year: 2023, Volume and Issue: 138(12)

Published: Dec. 16, 2023

Abstract In this study, we explore the emergence of amplitude-modulated bursting in a multi-frequency excited Liénard system. Our investigation reveals that system exhibits distinct patterns for lower damping value and varying forcing frequencies Conversely, higher with frequencies, intricate accompanied by variety oscillations. The discrete arise as consequence dynamic interplay slowly multiple frequency within To gain deeper understanding these dynamics, conduct comprehensive stability bifurcation analysis. Furthermore, to validate our findings, perform numerical simulations corroborate results through real-time hardware circuit experiment. This interdisciplinary approach provides valuable insights into behavior under excitation, shedding light on its complex dynamical characteristics.

Language: Английский

Citations

4
Pulse-shaped explosion-induced and non-pulse-shaped explosion-induced bursting dynamics in a parametrically and externally forced Rayleigh–van der Pol oscillator DOI

Chun Zhang,

Qiaoxia Tang,

Zhixiang Wang

et al.

Nonlinear Dynamics, Journal Year: 2022, Volume and Issue: 111(7), P. 6199 - 6211

Published: Dec. 13, 2022

Language: Английский

Citations

2
Complex bifurcation structures and bursting oscillations of an extended Duffing‐van der Pol oscillator DOI
Chun Zhang, Xindong Ma,

Qiaoxia Tang

et al.

Mathematical Methods in the Applied Sciences, Journal Year: 2022, Volume and Issue: unknown

Published: Dec. 8, 2022

This work focuses on the compound bursting dynamics and their generation mechanisms in an extended Duffing‐van der Pol oscillator excited by parametrical external slow‐varying excitations. By considering cosine excitation as a slow‐changing variables using Melnikov criterion, fold, Hopf, Homoclinic bifurcation critical conditions of generalized autonomous system are obtained, sets separate whole parameter plane into seven different areas. Based that, five patterns, i.e., “supHopf/supHopf” type, “fold/fold” “fold/Homoclinic” type via two hysteresis loops, “fold/supHopf‐supHopf/Homoclinic” loops “fold/supHopf” three studied. In addition, mechanism period motion is also investigated overlapping projection space to diagrams. Our research shows that oscillations sensitive , especially for small values . Moreover, this explicates how choice parameters affects trends slow manifolds. Finally, numerical simulations used illustrate test correctness work.

Language: Английский

Citations

2
Driven Force Induced Bifurcation Delay on the Chaotic Financial System DOI Creative Commons
Balamurali Ramakrishnan, Mohamed Abdalla, Salah Boulaaras

et al.

Complexity, Journal Year: 2022, Volume and Issue: 2022(1)

Published: Jan. 1, 2022

To understand the variations in financial characteristics, we examine dynamical behaviors by considering chaotic model with external force. First, characteristics are analyzed introducing driven force price index commodity demand. We discover that presence of an causes alternate occurrence oscillatory and steady states as a function time. Interestingly, find existence bifurcation delay (BD) during transition from (OS) to state (SS) or vice versa. Bifurcation is phenomenon which does not occur at actual point but rather later time, referred delay. confirm bifurcation, estimate compare it observed transition. Furthermore, delay, time between each consecutive cycle random fluctuations BD. Following that, BD virtualized via transformed phase portrait. In addition, show decreasing value average while increasing frequency forcing. Second, explored incorporating forces into investment demand unit cost. similar constant

Language: Английский

Citations

1
Complex bursting oscillations induced by pulse-shaped explosion and integer frequency ratios in a Rayleigh–van der Pol system DOI

Chen Zhang-Yao,

Xindong Ma, Qinsheng Bi

et al.

Pramana, Journal Year: 2023, Volume and Issue: 97(3)

Published: July 17, 2023

Language: Английский

Citations

0
On the occurrence of bursting oscillations in the damping Helmholtz–Rayleigh–Duffing oscillator with slow-changing parametrical and external forcings DOI
Chun Zhang,

Qiaoxia Tang

Physica Scripta, Journal Year: 2023, Volume and Issue: 99(1), P. 015204 - 015204

Published: Dec. 6, 2023

Abstract Multiple timescale effects can be reflected bursting oscillations in many classical nonlinear oscillators. In this work, we are concerned about the induced by two damped Helmholtz-Rayleigh-Duffing oscillator (written as DHRDO for short) excited slow-changing parametrical and external forcings. By using trigonometric function variation authenticating slow excitations a slowly varying state variable, time-varying rewritten new time-invariant system. Then, critical conditions of some typical bifurcations presented bifurcation theory. With help analyses, six patterns, i.e., ‘Hopf/Hopf-Hopf/Hopf’ bursting, ‘fold/Homoclinic-Hopf/Hopf’ ‘fold/Homoclinic/Hopf’ ‘Hopf/fold/Homoclinic/Hopf’ ‘Hopf/Homoclinic/Homoclinic/Hopf’ ‘Hopf/Homoclinic/Hopf-Hopf/Homoclinic/Hopf’ explored slow/fast decomposition method other techniques. Our findings provide different forms oscillation modes well patterns. addition, use numerical simulation to prove correctness theoretical analyses.

Language: Английский

Citations

0