Solvable limit cycle in a Volterra-type model of interacting populations

1975 ◽  
Vol 23 (3-4) ◽  
pp. 273-279 ◽  
Author(s):  
William B. Strickfaden ◽  
Bruce A. Lawrence
Keyword(s):  
Limit Cycle ◽  
Type Model ◽  
Volterra Type ◽  
Interacting Populations

scholarly journals A Ratio-Dependent Model of Replicator-Genetic Parasite Coevolution Demonstrates Instability of the Parasite-Free State

2021 ◽  
Author(s):  
Faina Berezovskaya ◽  
Georgy P. Karev ◽  
Eugene V. Koonin
Keyword(s):  
Mortality Rate ◽  
Carrying Capacity ◽  
Biological Evolution ◽  
Type Model ◽  
Model Parameters ◽  
Volterra Type ◽  
Dependent Model ◽  
Ratio Dependent ◽  
Host Parasite ◽  
Intrinsic Feature

AbstractNearly all organisms on earth are hosts to diverse genetic parasites including viruses and various types of mobile genetic elements. The emergence and persistence of genetic parasites was hypothesized to be an intrinsic feature of biological evolution. Here we examine this proposition by analysis of a ratio-dependent Lotka-Volterra type model of replicator(host)-parasite coevolution where the evolutionary outcome depends on the ratio of the host and parasite numbers. In a large, unbounded domain of the space of the model parameters, which include the replicator carrying capacity, the damage inflicted by the parasite, the replicative advantage of the parasites, and its mortality rate, the parasite-free equilibrium takes the form of a saddle and accordingly is unstable. Therefore, the evolutionary outcome is either the stable coexistence of the replicator and the parasite or extinction of both. Thus, the results of ratio-dependent model analysis are compatible with the hypothesis that genetic parasites are inherent to life.

scholarly journals Analysis of a Nonautonomous Delayed Predator-Prey System with a Stage Structure for the Predator in a Polluted Environment

2010 ◽  
Vol 2010 ◽  
pp. 1-18 ◽  
Author(s):  
G. P. Samanta
Keyword(s):  
Sufficient Conditions ◽  
Stage Structure ◽  
Positive Periodic Solution ◽  
Type Model ◽  
Predator Population ◽  
Constant Delay ◽  
Volterra Type ◽  
Globally Asymptotically Stable ◽  
Predator Prey ◽  
Prey System

A two-species nonautonomous Lotka-Volterra type model with diffusional migration among the immature predator population, constant delay among the matured predators, and toxicant effect on the immature predators in a nonprotective patch is proposed. The scale of the protective zone among the immature predator population can be regulated through diffusive coefficientsDi(t),i=1,2. It is proved that this system is uniformly persistent (permanence) under appropriate conditions. Sufficient conditions are derived to confirm that if this system admits a positive periodic solution, then it is globally asymptotically stable.

scholarly journals Markovian lifts of positive semidefinite affine Volterra-type processes

2019 ◽  
Vol 42 (2) ◽  
pp. 407-448 ◽  
Author(s):  
Christa Cuchiero ◽  
Josef Teichmann
Keyword(s):  
Partial Differential Equations ◽  
Differential Equations ◽  
Stochastic Partial Differential Equations ◽  
Positive Semidefinite ◽  
Point Of View ◽  
Type Model ◽  
Volterra Type ◽  
Partial Differential ◽  
Positive Semidefinite Matrices ◽  
Feller Property

Abstract We consider stochastic partial differential equations appearing as Markovian lifts of matrix-valued (affine) Volterra-type processes from the point of view of the generalized Feller property (see, e.g., Dörsek and Teichmann in A semigroup point of view on splitting schemes for stochastic (partial) differential equations, 2010. arXiv:1011.2651). We introduce in particular Volterra Wishart processes with fractional kernels and values in the cone of positive semidefinite matrices. They are constructed from matrix products of infinite dimensional Ornstein–Uhlenbeck processes whose state space is the set of matrix-valued measures. Parallel to that we also consider positive definite Volterra pure jump processes, giving rise to multivariate Hawkes-type processes. We apply these affine covariance processes for multivariate (rough) volatility modeling and introduce a (rough) multivariate Volterra Heston-type model.

DESYNCHRONIZATION AND DECOUPLING OF INTERACTING OSCILLATORS BY NONLINEAR DELAYED FEEDBACK

2006 ◽  
Vol 16 (07) ◽  
pp. 1977-1987 ◽  
Author(s):  
OLEKSANDR V. POPOVYCH ◽  
CHRISTIAN HAUPTMANN ◽  
PETER A. TASS
Keyword(s):  
Deep Brain Stimulation ◽  
Limit Cycle ◽  
Brain Stimulation ◽  
Control Method ◽  
Neurological Diseases ◽  
Mean Field ◽  
Stimulation Parameter ◽  
Interacting Populations ◽  
Parameter Variations ◽  
Deep Brain

A novel control method for desynchronization of strongly synchronized populations of interacting oscillators is described. We show that an ensemble's mean field, nonlinearly processed and fed back into the ensemble, causes an effective desynchronization. The method is mild, demand controlled, and robust against system and stimulation parameter variations. The desynchronization and decoupling effects of the method are illustrated by examples of one and two interacting populations of limit-cycle oscillators. We suggest our method for mild and effective deep brain stimulation in neurological diseases characterized by pathological cerebral synchronization.

A Volterra type model for image processing

1998 ◽  
Vol 7 (3) ◽  
pp. 292-303 ◽  
Author(s):  
G.H. Cottet ◽  
M.E. Ayyadi
Keyword(s):  
Image Processing ◽  
Type Model ◽  
Volterra Type

scholarly journals A note on the stability of a modified Lotka-Volterra model using Hurwitz polynomials

2021 ◽  
Vol 20 ◽  
pp. 431-441
Author(s):  
Fabián Toledo , Sánchez ◽  
Pedro Pablo Cárdenas Alzate ◽  
Carlos Arturo Escudero Salcedo
Keyword(s):  
Differential Equations ◽  
Initial Conditions ◽  
Stability Study ◽  
Volterra Model ◽  
Type Model ◽  
Stability Criteria ◽  
Volterra Type ◽  
Hurwitz Polynomials ◽  
Intuitive Idea ◽  
The Stability

In the analysis of the dynamics of the solutions of ordinary differential equations we can observe whether or not small variations or perturbations in the initial conditions produce small changes in the future; this intuitive idea of stability was formalized and studied by Lyapunov, who presented methods for the stable analysis of differential equations. For linear or nonlinear systems, we can also analyze the stability using criteria to obtain Hurwitz type polynomials, which provide conditions for the analysis of the dynamics of the system, studying the location of the roots of the associated characteristic polynomial. In this paper we present a stability study of a Lotka-Volterra type model which has been modified considering the carrying capacity or support in the prey and time delay in the predator, this stable analysis is performed using stability criteria to obtain Hurwitz-type polynomials.

scholarly journals Canard doublet in a Lotka-Volterra type model

2008 ◽  
Vol 138 ◽  
pp. 012019 ◽  
Author(s):  
A Pokrovskii ◽  
E Shchepakina ◽  
V Sobolev
Keyword(s):  
Type Model ◽  
Volterra Type
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