Asymptotically Stable Almost-Periodic Oscillations in Systems with Hysteresis Nonlinearities

2000 ◽  
Vol 19 (2) ◽  
pp. 469-487 ◽  
Author(s):  
M. Brokate ◽  
I. Collings ◽  
A.V. Pokrovskii ◽  
F. Stagnitti
Keyword(s):  
Asymptotically Stable ◽  
Almost Periodic ◽  
Periodic Oscillations

scholarly journals Permanence and Almost Periodic Solution for an Enterprise Cluster Model Based on Ecology Theory with Feedback Controls on Time Scales

2013 ◽  
Vol 2013 ◽  
pp. 1-14 ◽  
Author(s):  
Yuanhong Zhi ◽  
Zunling Ding ◽  
Yongkun Li
Keyword(s):  
Periodic Solution ◽  
Time Scales ◽  
Cluster Model ◽  
Sufficient Conditions ◽  
Almost Periodic Solution ◽  
Asymptotically Stable ◽  
Almost Periodic ◽  
Feedback Controls ◽  
Competition And Cooperation ◽  
Enterprise Cluster

We present a model with feedback controls based on ecology theory, which effectively describes the competition and cooperation of enterprise cluster in real economic environments. Applying the comparison theorem of dynamic equations on time scales and constructing a suitable Lyapunov functional, sufficient conditions which guarantee the permanence and the existence of uniformly asymptotically stable almost periodic solution of the system are obtained.

scholarly journals Almost Periodic Solution of a Multispecies Discrete Mutualism System with Feedback Controls

2015 ◽  
Vol 2015 ◽  
pp. 1-14 ◽  
Author(s):  
Hui Zhang ◽  
Feng Feng ◽  
Bin Jing ◽  
Yingqi Li
Keyword(s):  
Numerical Simulation ◽  
Periodic Solution ◽  
Lyapunov Function ◽  
Sufficient Conditions ◽  
Almost Periodic Solution ◽  
Asymptotically Stable ◽  
Almost Periodic ◽  
Feedback Controls ◽  
Positive Almost Periodic Solution ◽  
Mutualism System

We consider an almost periodic multispecies discrete Lotka-Volterra mutualism system with feedback controls. We firstly obtain the permanence of the system by utilizing the theory of difference equation. By means of constructing a suitable Lyapunov function, sufficient conditions are obtained for the existence of a unique positive almost periodic solution which is uniformly asymptotically stable. An example together with numerical simulation indicates the feasibility of the main result.

scholarly journals Global Analysis of Almost Periodic Solution of a Discrete Multispecies Mutualism System

2014 ◽  
Vol 2014 ◽  
pp. 1-12 ◽  
Author(s):  
Hui Zhang ◽  
Bin Jing ◽  
Yingqi Li ◽  
Xiaofeng Fang
Keyword(s):  
Periodic Solution ◽  
Global Analysis ◽  
Sufficient Conditions ◽  
Almost Periodic Solution ◽  
Asymptotically Stable ◽  
Almost Periodic ◽  
Periodic Sequences ◽  
Almost Periodic Sequences ◽  
Globally Attractive ◽  
Mutualism System

This paper discusses a discrete multispecies Lotka-Volterra mutualism system. We first obtain the permanence of the system. Assuming that the coefficients in the system are almost periodic sequences, we obtain the sufficient conditions for the existence of a unique almost periodic solution which is globally attractive. In particular, for the discrete two-species Lotka-Volterra mutualism system, the sufficient conditions for the existence of a unique uniformly asymptotically stable almost periodic solution are obtained. An example together with numerical simulation indicates the feasibility of the main result.

An asymptotic analysis of the Sal’nikov thermokinetic oscillator

1988 ◽  
Vol 416 (1851) ◽  
pp. 425-441 ◽  
Keyword(s):  
Fuel Consumption ◽  
Thermal Explosion ◽  
Homoclinic Bifurcation ◽  
Exact Results ◽  
Asymptotically Stable ◽  
Almost Periodic ◽  
Periodic Behaviour ◽  
Limiting Case ◽  
Dimensionless Heat ◽  
Thermal Explosion Theory

The Sal’nikov thermokinetic oscillator is studied in the limiting case where the dimensionless heat capacity tends to zero. This is equivalent to the ‘no fuel consumption’ approximation in classical thermal explosion theory and is equally revealing in that many exact results can be obtained by simple algebraic methods. Regions in parameter space are found where, although the system is asymptotically stable, a large single excursion occurs before the steady state is approached. These regions border the region of oscillations which in the limiting case are of the relaxation type. All the interesting behaviour requires RT / E < 1/4, an obvious parallel with thermal explosion theory. The unstable limit cycles that occur in the Sal’nikov oscillator disappear in this limiting case. However, the requirements for an unstable limit cycle to exist in the ‘relaxation’ limit are discussed. The homoclinic bifurcation in the limiting case is also examined and it is shown that this bifurcation can (in theory) be calculated exactly. In addition, an extension to the Sal’nikov oscillator scheme in a closed system to include fuel consumption is studied both numerically and in a limiting case. It is shown that the full scheme exhibits finite trains of almost periodic behaviour before monotonically approaching equilibrium.

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