1,721,276 research outputs found
How to Construct Complex Dynamics? A Note on a Topological Approach
No full textWe investigate the presence of complex behaviors for the solutions of two different dynamical systems: one is of discrete type and the other is continuous. We give evidence of "chaos" in the framework of topological horseshoes and show how different problems can be analyzed by the same procedure
Stationary fronts and pulses for multistable equations with saturating diffusion
No full textWe deal with stationary solutions of a reaction-diffusion equation with flux-saturated diffusion and multistable reaction term, in dependence on a positive parameter ε. Motivated by previous numerical results obtained by A. Kurganov and P. Rosenau (Nonlinearity, 2006), we investigate stationary solutions of front and pulse-type and discuss their qualitative features. We study the limit of such solutions for ε→0, showing that, in spite of the wide variety of profiles that can be constructed, there is essentially a unique configuration in the limit for both stationary fronts and pulses. We finally discuss some variational features that include the case where the solutions having continuous energy may not be global minimizers of the associated action functional
About Chaotic Dynamics in the Twisted Horseshoe Map
No full textThe twisted horseshoe map was developed in order to study a class of density dependent Leslie population models with two age classes. From the beginning, scientists have tried to prove that this map presents chaotic dynamics. Some demonstrations that have appeared in mathematical literature present some difficulties or delicate issues. In this paper, we give a simple and rigorous proof based on a different approach. We also highlight the possibility of getting chaotic dynamics for a broader class of maps
A negative answer to a conjecture arising in the study of selection migration models in population genetics
No full textWe deal with the study of the evolution of the allelic frequencies, at a single locus, for a population distributed continuously over a bounded habitat. We consider evolution which occurs under the joint action of selection and arbitrary migration, that is independent of genotype, in absence of mutation and random drift. The focus is on a conjecture, that was raised up in literature of population genetics, about the possible uniqueness of polymorphic equilibria, which are known as clines, under particular circumstances. We study the number of these equilibria, making use of topological tools, and we give a negative answer to that question by means of two examples. Indeed, we provide numerical evidence of multiplicity of positive solutions for two different Neumann problems satisfying the requests of the conjecture
Ambrosetti-Prodi type result to a Neumann problem via a topological approach
No full textWe prove an Ambrosetti-Prodi type result for a Neumann problem associated to the equation u + f(x, u(x)) = μ when the nonlinearity has the following form: f(x, u):= a(x)g(u) − p(x). The assumptions considered generalize the classical one, f(x, u) → +∞ as |u| → +∞, without requiring any uniformity condition in x. The multiplicity result which characterizes these kind of problems will be proved by means of the shooting method
Chaos in periodically forced reversible vector fields
No full textWe discuss the appearance of chaos in time-periodic perturbations of reversible vector fields in the plane. We use the normal forms of codimension 1 reversible vector fields and discuss the ways a time-dependent periodic forcing term of pulse form may be added to them to yield topological chaotic behaviour. Chaos here means that the resulting dynamics is semiconjugate to a shift in a finite alphabet. The results rely on the classification of reversible vector fields and on the theory of topological horseshoes. This work is part of a project of studying periodic forcing of symmetric vector fields
Wavefronts for Generalized Perona-Malik Equations
No full textWe consider a generalization of Perona-Malik equation with reaction and convective terms. By assuming that the reaction is monostable, we prove the existence of regular wavefronts as well as some of their qualitative properties. It turns out that the admissible speeds for subcritical or critical wavefronts form a closed half-line; the threshold cannot be computed explicitly but an estimate is provided. Moreover, the wavefronts are strictly monotone and their slope is bounded by the critical values of the diffusion
Wavefront solutions to reaction-convection equations with Perona-Malik diffusion
No full textWe study a nonlinear reaction-convection equation with a degenerate diffusion of Perona-Malik's type and a monostable reaction term. Under quite general assumptions, we show the presence of wavefront solutions and prove their main properties. In particular, such wavefronts exist for every speed in a closed half-line and we give estimates of the threshold speed. The wavefront profiles are also strictly monotone and their slopes are uniformly bounded by the critical values of the diffusion
Ambrosetti–Prodi Periodic Problem Under Local Coercivity Conditions
Full text linkAbstract
In this paper we focus on the periodic boundary value problem associated with the Liénard differential equation
x
′′
+
f
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x
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x
′
+
g
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t
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x
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=
s
{x^{\prime\prime}+f(x)x^{\prime}+g(t,x)=s}
, where s is a real parameter, f and g are continuous functions and g is T-periodic in the variable t. The classical framework of Fabry, Mawhin and Nkashama, related to the Ambrosetti–Prodi periodic problem, is modified to include conditions without uniformity, in order to achieve the same multiplicity result under local coercivity conditions on g. Analogous results are also obtained for Neumann boundary conditions.</jats:p
Extinction or coexistence in periodic kolmogorov systems of competitive type
Full text linkWe study a periodic Kolmogorov system describing two species nonlinear competition. We discuss coexistence and extinction of one or both species, and describe the domain of attraction of nontrivial periodic solutions in the axes, under conditions that generalise Gopalsamy conditions. Finally, we apply our results to a model of microbial growth and to a model of phyto- plankton competition under the effect of toxins
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