scholarly journals Asymptotic analysis of internal relaxation oscillations in a conceptual climate model

2020 ◽  
Vol 85 (3) ◽  
pp. 467-494
Author(s):  
Łukasz Płociniczak
Keyword(s):  
Asymptotic Analysis ◽  
Climate Model ◽  
Stable Limit Cycle ◽  
Stable Limit ◽  
External Forcing ◽  
Relaxation Oscillations ◽  
Robust Model ◽  
Wide Range ◽  
Paleoclimatic Data ◽  
The Stability

Abstract We construct a dynamical system based on the Källén–Crafoord–Ghil conceptual climate model which includes the ice–albedo and precipitation–temperature feedbacks. Further, we classify the stability of various critical points of the system and identify a parameter which change generates a Hopf bifurcation. This gives rise to a stable limit cycle around a physically interesting critical point. Moreover, it follows from the general theory that the periodic orbit exhibits relaxation-oscillations that are a characteristic feature of the Pleistocene ice ages. We provide an asymptotic analysis of their behaviour and derive a formula for the period along with several estimates. They, in turn, are in a decent agreement with paleoclimatic data and are independent of any parametrization used. Whence, our simple but robust model shows that a climate may exhibit internal relaxation oscillations without any external forcing and for a wide range of parameters.

scholarly journals STUDYING THE STABILITY BY USING LOCAL LINEARIZATION METHOD

2020 ◽  
Vol 2 (1) ◽  
pp. 27-31
Author(s):  
Abdulghafoor Jasim Salim ◽  
Kais Ismail Ebrahem ◽  
Suhirman
Keyword(s):  
Singular Point ◽  
Limit Cycle ◽  
Autoregressive Model ◽  
Stable Limit Cycle ◽  
Linearization Method ◽  
Stable Limit ◽  
Local Linearization ◽  
Non Linear ◽  
The Stability ◽  
Local Linearization Method

Abstract: In this paper we study the stability of one of a non linear autoregressive model with trigonometric term  by using local linearization method proposed by Tuhro Ozaki .We find the singular point ,the stability of the singular point and the limit cycle. We conclude  that the proposed model under certain conditions have a non-zero singular point which is  a asymptotically salable ( when  0 ) and have an  orbitaly stable limit cycle . Also we give some examples in order to explain the method. Key Words : Non-linear Autoregressive model; Limit cycle; singular point; Stability.

Energy harvesting for actuators and sensors using free-floating flaps

2016 ◽  
Vol 28 (2) ◽  
pp. 163-177 ◽  
Author(s):  
Lars O Bernhammer ◽  
Roeland De Breuker ◽  
Moti Karpel
Keyword(s):  
Limit Cycle ◽  
Vibrational Energy ◽  
Stable Limit Cycle ◽  
Electric Circuit ◽  
Electronic System ◽  
Rotational Axis ◽  
Stable Limit ◽  
Limit Cycle Oscillations ◽  
Trailing Edge ◽  
The Stability

A novel configuration of an energy harvester for local actuation and sensing devices using limit cycle oscillations has been modeled, designed and tested. A wing section has been designed with two trailing-edge free-floating flaps. A free-floating flap is a flap that can freely rotate around a hinge axis and is driven by trailing edge tabs. In the rotational axis of each flap a generator is mounted that converts the vibrational energy into electricity. It has been demonstrated numerically how a simple electronic system can be used to keep such a system at stable limit cycle oscillations by varying the resistance in the electric circuit. Additionally, it was shown that the stability of the system is coupled to the charge level of the battery, with increasing charge level leading to a less stable system. The system has been manufactured and tested in the Open Jet Wind Tunnel Facility of the Technical University Delft. The numerical results could be validated successfully and voltage generation could be demonstrated at cost of a decrease in lift of 2%.

scholarly journals An analysis of instabilities and limit cycles in glacier-dammed reservoirs

2019 ◽  
Author(s):  
Christian Schoof
Keyword(s):  
Limit Cycle ◽  
Limit Cycles ◽  
Water Storage ◽  
Drainage System ◽  
Stable Limit Cycle ◽  
Stable Limit ◽  
Outburst Floods ◽  
The World ◽  
The Stability ◽  
Glacial Hazards

Abstract. Glacier lake outburst floods are common glacial hazards around the world. How big such floods can become (either in terms of peak discharge or in terms of total volume released) depends on how they are initiated: what causes the runaway enlargement of a subglacial or other conduit to start, and how big can the lake get before that point is reached? Here we investigate how the spontaneous channelization of a linked-cavity drainage system controls the onset of floods. In agreement with previous work, we show that floods only occur in a band of water throughput rates, and identify stabilizing mechanisms that allow steady drainage of an ice-dammed reservoir. We also show how stable limit cycle solutions emerge from the instability, a show how and why the stability properties of a drainage system with spatially spread-out water storage differ from those where storage is localized in a single reservoir or lake.

scholarly journals Levitation Stability and Hopf Bifurcation of EMS Maglev Trains

2020 ◽  
Vol 2020 ◽  
pp. 1-12 ◽  
Author(s):  
Junxiong Hu ◽  
Weihua Ma ◽  
Xiaohao Chen ◽  
Shihui Luo
Keyword(s):  
Hopf Bifurcation ◽  
Stable Limit Cycle ◽  
Coupled System ◽  
Stable Limit ◽  
Maglev Train ◽  
Real Time System ◽  
Levitation System ◽  
The Stability ◽  
Control Feedback ◽  
Track Beam

This paper analyzed the mechanical characteristics of single electromagnet system and elastic track beam of EMS maglev train and established a five-dimensional dynamics model of single electromagnet-track beam coupled system with classical PD control strategy adopted for its levitation system. Then, based on the Hurwitz criterion and the high-dimensional Hopf bifurcation theory, the stability of the coupled system is analyzed; the existence of the Hopf bifurcation is discussed and the bifurcation direction and the stability of the periodic solution are determined with levitation control feedback coefficient kp as the bifurcation parameter; and numerical simulation is conducted to verify the validity of the theoretical analysis results. The results show that the Hurwitz algebra criterion can directly determine the eigenvalues and symbols of the dynamics system to facilitate the analysis on the stability of the system and the Hopf bifurcation without the necessity of calculating the specific eigenvalues; supercritical Hopf bifurcation will occur under the given parameters, that is, when kp<kp0, the real-time system is asymptotically stable, yet Hopf bifurcation occurs as kp increases gradually beyond kp0, with the stability of the system lost and a stable limit cycle branched.

Inducing sustained oscillations in a class of nonlinear discrete time systems

2016 ◽  
Vol 24 (6) ◽  
pp. 1162-1170 ◽  
Author(s):  
AR Hakimi ◽  
T Binazadeh
Keyword(s):  
Limit Cycle ◽  
Discrete Time ◽  
Stable Limit Cycle ◽  
Domain Of Attraction ◽  
Stable Limit ◽  
Discrete Time System ◽  
Sustained Oscillations ◽  
Discrete Time Systems ◽  
The Stability ◽  
Time Systems

Inducing sustained oscillations in a class of nonlinear discrete time systems is studied in this paper. The novelty of this paper is based on the proposed approach in generating stable oscillations according to limit cycle control. The limit cycle control is not formulated for nonlinear discrete time systems of any order and this paper concentrates on this issue. Considering the stable limit cycle as a positive limit set for the dynamical system, a nonlinear control law is designed to create the considered limit cycle in the phase trajectories of the closed-loop nonlinear discrete time system to achieve oscillations with the desirable amplitude and frequency. For this purpose, firstly, the limit cycle control is proposed for second-order nonlinear discrete time systems. The stability analysis of the generated limit cycle is done via a suitable Lyapunov function. Also, the domain of attraction of the created limit cycle is calculated. The proposed method is then extended for nonlinear discrete time systems of any order via the backstepping technique. Finally, computer simulations are performed for a practical example to demonstrate the ability of the designed controller in generating stable oscillations.

scholarly journals Stability analysis of shock response of EV powertrain considering electro-mechanical coupling effect

2021 ◽  
Vol 13 (8) ◽  
pp. 168781402110371
Author(s):  
Qingzhen Han ◽  
Shiqin Niu ◽  
Jie You
Keyword(s):  
Coupling Effect ◽  
Equilibrium Points ◽  
Stable Limit Cycle ◽  
Central Point ◽  
Stable Limit ◽  
Mechanical Coupling ◽  
Saddle Node ◽  
Shock Response ◽  
Response Equation ◽  
The Stability

The main purpose of this manuscript is to analyze the stability of the shock response of the electric vehicle (EV) powertrain when considering the electro-mechanical coupling effect. The nonlinear drive-shaft model of the powertrain is built using the Lagrange method, based on which the shock response equation is also deduced. Meanwhile, the number and properties of the equilibrium points are studied. Two kinds of equilibrium points, saddle node and central point, which can induce different dynamic behaviors are found. The simulation results show that the trajectory of the shock response may be unstable if the parameters are chosen in the region that has a saddle node. If the parameters of the powertrain fall into the region that has only one central point, the trajectory of the shock response will be attracted by the stable limit cycle. Therefore, to ensure that the shock response is more stable, the parameters should be chosen in the region where only one central point is present.

scholarly journals A Control Framework for Anthropomorphic Biped Walking Based on Stabilizing Feedforward Trajectories

2016 ◽  
Author(s):  
Siavash Rezazadeh ◽  
Robert D. Gregg
Keyword(s):  
Stable Limit Cycle ◽  
Humanoid Robots ◽  
Stable Limit ◽  
Dynamic Walking ◽  
Bipedal Robots ◽  
Bipedal Robot ◽  
External Perturbations ◽  
Control Framework ◽  
Zero Moment ◽  
The Stability

Although dynamic walking methods have had notable successes in control of bipedal robots in the recent years, still most of the humanoid robots rely on quasi-static Zero Moment Point controllers. This work is an attempt to design a highly stable controller for dynamic walking of a human-like model which can be used both for control of humanoid robots and prosthetic legs. The method is based on using time-based trajectories that can induce a highly stable limit cycle to the bipedal robot. The time-based nature of the controller motivates its use to entrain a model of an amputee walking, which can potentially lead to a better coordination of the interaction between the prosthesis and the human. The simulations demonstrate the stability of the controller and its robustness against external perturbations.

OSCILLATIONS IN DELAY DIFFERENTIAL EQUATION MODEL OF REPRODUCTIVE HORMONES IN MEN WITH COMPUTER SIMULATIONS

1994 ◽  
Vol 02 (01) ◽  
pp. 73-90 ◽  
Author(s):  
PRITHA DAS ◽  
A.B. ROY
Keyword(s):  
Stable Limit Cycle ◽  
Equation Model ◽  
Reproductive Hormones ◽  
Phase Portraits ◽  
Stable Limit ◽  
Delay Model ◽  
Local Asymptotic Stability ◽  
The Stability ◽  
Linearized Model ◽  
Delay Differential

We produce here a delay model to explain the control of testosterone secretion. We have modified our earlier model by incorporating one negative feedback function which explains the inhibition of the pituitary secretion of the hormone LH (Luteinizing hormone) by the local testosterone concentration. We have derived the conditions for local asymptotic stability and switching to instability of the steady state. The length of the delay preserving the stability has also been derived. Lastly the conditions for instability and bifurcation results have been derived for the linearized model. Phase portraits of the original nonlinear model showing stable limit cycle have been simulated.

An Analysis of Micro Aeroelastic Energy Harvesting Devices

2009 ◽  
Author(s):  
Daniel G. Cole ◽  
Lisa M. Weiland
Keyword(s):  
Power Generation ◽  
Renewable Energy ◽  
Energy Harvesting ◽  
Limit Cycle ◽  
Stable Limit Cycle ◽  
Stable Limit ◽  
Energy Harvesters ◽  
The Stability ◽  
Energy Harvesting Devices ◽  
Multi Mode

New micro renewable energy harvesting devices are being developed using the stable limit cycle response of aeroelastic systems to drive energy conversion. This paper analyzes such devices. This paper investigates devices that use two types of aeroelastic instability: galloping and multi-mode flutter. Since the generation of power can be stabilizing, resulting in no power generation at all, the analysis begins by analyzing the stability of such devices from the perspective of power generation. Next, the level of power generation is discussed, and peak levels of performance are found. The analysis suggests that with proper tuning the power generation of micro aeroelastic energy harvesters operating at representative speeds (∼4.5 m/s (10 mph)) can produce power on the order of 10 mW.

scholarly journals Stable Polymorphisms in a Two-Locus Gene-for-Gene System

2005 ◽  
Vol 95 (7) ◽  
pp. 728-736 ◽  
Author(s):  
J. Segarra
Keyword(s):  
Initial Conditions ◽  
Stable Limit Cycle ◽  
Infinite Family ◽  
Host Population ◽  
Stable Limit ◽  
Final State ◽  
Closed Curves ◽  
Interior Equilibrium ◽  
Wide Range ◽  
Gene For Gene

A two-locus gene-for-gene model is presented to analyze coevolutionary dynamics in interactions between host plants and their pathogens. Using both analytical and simulation approximations, we show that the behavior of the model is very simple with one locus. In the reciprocal genetic feedback version, there is a smooth outward spiral toward the boundaries. In the delayed feedback version, there is an infinite family of closed curves corresponding to different initial conditions. Both versions of the model are stabilized by the addition of recurrent mutation. Either a stable interior equilibrium or a stable limit cycle appears. But with the two-locus model, different coevolutionary outcomes are predicted according to the parameter values. For a wide range of small and medium values of virulence and resistance costs, complex fluctuations arise. The number of virulence alleles per isolate and the number of resistance alleles per plant cycle indefinitely. If the costs of both virulence and resistance are above a threshold, the final state of the coevolutionary dynamics is a stable single-resistance static polymorphism in the host and avirulence in the parasite. An equivalent threshold to maintain a disease-free host population was obtained analytically for a multilocus system. These expressions can be used to determine the number of single-resistance host genotypes that would have to be present in a mixture to prevent the spread of any virulent race of pathogen. The model demonstrates that it is preferable to use mixtures of single-resistant genotypes rather than using multiple resistance alleles in the same cultivar.

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