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We study the dynamics of a two-planet system, which evolves being in a $1/1$ mean motion resonance (co-orbital motion) with non-zero mutual inclination. In particular, we examine the existence of bifurcations of periodic orbits from the…
This paper deals with the existence, multiplicity, minimal complexity and global structure of the subharmonic solutions to a class of planar Hamiltonian systems with periodic coefficients, being the classical predator-prey model of V.…
We consider the general spatial three body problem and study the dynamics of planetary systems consisting of a star and two planets which evolve into 2/1 mean motion resonance and into inclined orbits. Our study is focused on the periodic…
Foraging movements of predator play an important role in population dynamics of prey-predator interactions, which have been considered as mechanisms that contribute to spatial self-organization of prey and predator. In nature, there are…
We study a mathematical model of environments populated by both preys and predators, with the possibility for predators to actively compete for the territory. For this model we study existence and uniqueness of solutions, and their…
This paper examines a discrete predator-prey model that incorporates prey refuge and its detrimental impact on the growth of the prey population. Age structure is taken into account for predator species. Furthermore, juvenile hunting as…
An age-structured predator-prey system with diffusion and Holling-Tanner-type nonlinearities is considered. Regarding the intensity of the fertility of the predator as bifurcation parameter, we prove that a branch of positive coexistence…
We examine the interaction of transcritical and saddle-node bifurcations in a predator-prey-nutrient system that is stressed by the presence of a toxicant affecting the prey. This model, formulated by Kooi et al. ({\sl Ecol. Model.} {\bf…
In this paper, the dynamics of a modified Leslie-Gower predator-prey system with two delays and diffusion is considered. By calculating stability switching curves, the stability of positive equilibrium and the existence of Hopf bifurcation…
Double Hopf bifurcation analysis can be used to reveal some complicated dynamical behavior in a dynamical system, such as the existence or coexistence of periodic orbits, quasi-periodic orbits, or even chaos. In this paper, an algorithm for…
We investigate the emergence of complex dynamics in a system of coupled dissipative kicked rotors and show that critical transitions can be understood via bifurcations of simple states. We study multistability and bifurcations in the single…
Evolutionary dynamics provides an iconic relationship --- the periodic frequency of a game is determined by the payoff matrix of the game. This paper reports the first experimental evidence to demonstrate this relationship. Evidence comes…
A classical double oscillator model, that includes in certain parameter limits, the standard harmonic oscillator and the inverse oscillator, is interpreted as a dynamical system. We study its essential features and make a qualitative…
A discrete-time version of the replicator equation for two-strategy games is studied. The stationary properties differ from that of continuous time for sufficiently large values of the parameters, where periodic and chaotic behavior replace…
We provide an analytical proof of the existence of a stable periodic orbit contained in the region of coexistence of the three species of a tritrophic chain. The method used consists in analyzing a triple Hopf bifurcation. For some values…
Honest signals and cues have been observed as part of interspecific and intraspecific communication among animals. Recent theories suggest that existing signaling systems have evolved through natural selection imposed by predators. Honest…
Reaction-diffusion analytical modeling of predator-prey systems has shown that specialist natural enemies can slow, stop and even reverse pest invasions, assuming that the prey population displays a strong Allee effect in its growth. Few…
In this paper, dynamical systems theory and bifurcation theory are applied to investi- gate the rich dynamical behaviours observed in three simple disease models. The 2- and 3-dimensional models we investigate have arisen in previous…
The predator-prey dynamic appertaining to two species is explored, wherein the predator species is structured into different stages. As evidenced from natural documentation, the immature predators possess the potential to predate albeit not…
We construct a global bifurcation diagram of the plane differential system $$ {l} \dot x = x(1-x)-x y/(a+x^2), \dot y = y(\delta-\beta y/x), x(t)>0, y(t)>0, a>0, \delta>0, \beta>0, $$ which describes the predator-prey interaction.