Variations on Lyapunov's stability criterion and periodic prey-predator systems

نویسندگان

چکیده

<p style='text-indent:20px;'>A classical stability criterion for Hill's equation is extended to more general families of periodic two-dimensional linear systems. The results are motivated by the study mechanical vibrations with friction and prey-predator systems.</p>

برای دانلود باید عضویت طلایی داشته باشید

برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

منابع مشابه

Prey-Predator System; Having Stable Periodic Orbit

The study of differential equations is useful in to analyze the possible past or future with help of present information. In this paper, the behavior of solutions has been analyzed around the equilibrium points for Gause model. Finally, some results are worked out to exist the stable periodic orbit for mentioned predator-prey system.

متن کامل

Periodic Solutions in Periodic Delayed Gause-Type Predator-Prey Systems

Reasonable sufficient conditions are obtained for the existence of positive periodic solutions in periodic delayed Gause-type predator-prey systems. Our approach involves the application of coincidence degree theorem and estimations of uniform upper bounds on solutions. This method imposes minimum restrictions on the form and magnitude of time delays. Indeed, our results are applicable to discr...

متن کامل

The Stability of Some Systems of Harvested Lotka-Volterra Predator-Prey Equations

Some scientists are interesting to study in area of harvested ecological modelling. The harvested population dynamics is more realistic than other ecological models. In the present paper, some of the Lotka-Volterra predator-prey models have been considered. In the said models, existing species are harvested by constant or variable growth rates. The behavior of their solutions has been analyzed ...

متن کامل

Angular velocity variations and stability of spatially explicit prey-predator systems.

The linear instability of Lotka-Volterra orbits in the homogenous manifold of a two-patch system is analyzed. The origin of these orbits instability in the absence of prey migration is revealed to be the dependence of the angular velocity on the azimuthal angle; in particular, the system desynchronizes at the exit from the slow part of the trajectory. Using this insight, an analogous model of a...

متن کامل

Periodic travelling waves in cyclic predator-prey systems

Jonathan A. Sherratt Centre for Theoretical Modelling in Medicine, Department of Ma thema tie, Heriot-Watt University, Edinburgh EH14 4AS, U.K. E-mail: jasbma.hw.ac.uk Abstract Predation is an established cause of cycling in prey species. Here, the ability of predation to explain periodic travelling waves in prey populations, which have recently been found in a number of spatiotemporal field st...

متن کامل

ذخیره در منابع من


  با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید

ژورنال

عنوان ژورنال: Electronic research archive

سال: 2021

ISSN: ['2688-1594']

DOI: https://doi.org/10.3934/era.2021069