Abstract: In this paper, a magnetron memristor model based on hyperbolic sine function is presented and the correctness proved by studying the trajectory of its voltage and current phase, and then a memristor chaotic system with the memristor model is presented. The phase trajectories and the bifurcation diagrams and Lyapunov exponent spectrum of the magnetron memristor system are plotted by numerical simulation, and the chaotic evolution with changing the parameters of the system is also given. The paper includes numerical simulations and mathematical model, which confirming that the system, has a wealth of dynamic behavior.
Abstract: In population dynamics the study of both, the
abundance and the spatial distribution of the populations in a
given habitat, is a fundamental issue a From ecological point of
view, the determination of the factors influencing such changes
involves important problems. In this paper a mathematical model to
describe the temporal dynamic and the spatiotemporal dynamic of the
interaction of three populations (pollinators, plants and herbivores) is
presented. The study we present is carried out by stages: 1. The
temporal dynamics and 2. The spatio-temporal dynamics. In turn,
each of these stages is developed by considering three cases which
correspond to the dynamics of each type of interaction. For instance,
for stage 1, we consider three ODE nonlinear systems describing
the pollinator-plant, plant-herbivore and plant-pollinator-herbivore,
interactions, respectively. In each of these systems different types of
dynamical behaviors are reported. Namely, transcritical and pitchfork
bifurcations, existence of a limit cycle, existence of a heteroclinic
orbit, etc. For the spatiotemporal dynamics of the two mathematical
models a novel factor are introduced. This consists in considering
that both, the pollinators and the herbivores, move towards those
places of the habitat where the plant population density is high.
In mathematical terms, this means that the diffusive part of the
pollinators and herbivores equations depend on the plant population
density. The analysis of this part is presented by considering pairs of
populations, i. e., the pollinator-plant and plant-herbivore interactions
and at the end the two mathematical model is presented, these models
consist of two coupled nonlinear partial differential equations of
reaction-diffusion type. These are defined on a rectangular domain
with the homogeneous Neumann boundary conditions. We focused
in the role played by the density dependent diffusion term into
the coexistence of the populations. For both, the temporal and
spatio-temporal dynamics, a several of numerical simulations are
included.
Abstract: The customers use the best compromise criterion
between price and quality of service (QoS) to select or change
their Service Provider (SP). The SPs share the same market and
are competing to attract more customers to gain more profit. Due
to the divergence of SPs interests, we believe that this situation is a
non-cooperative game of price and QoS. The game converges to an
equilibrium position known Nash Equilibrium (NE). In this work, we
formulate a game theoretic framework for the dynamical behaviors
of SPs. We use Genetic Algorithms (GAs) to find the price and
QoS strategies that maximize the profit for each SP and illustrate
the corresponding strategy in NE. In order to quantify how this NE
point is performant, we perform a detailed analysis of the price of
anarchy induced by the NE solution. Finally, we provide an extensive
numerical study to point out the importance of considering price and
QoS as a joint decision parameter.
Abstract: The output error of the globoidal cam mechanism can
be considered as a relevant indicator of mechanism performance,
because it determines kinematic and dynamical behavior of
mechanical transmission. Based on the differential geometry and the
rigid body transformations, the mathematical model of surface
geometry of the globoidal cam is established. Then we present the
analytical expression of the output error (including the transmission
error and the displacement error along the output axis) by considering
different manufacture and assembly errors. The effects of the center
distance error, the perpendicular error between input and output axes
and the rotational angle error of the globoidal cam on the output error
are systematically analyzed. A globoidal cam mechanism which is
widely used in automatic tool changer of CNC machines is applied for
illustration. Our results show that the perpendicular error and the
rotational angle error have little effects on the transmission error but
have great effects on the displacement error along the output axis. This
study plays an important role in the design, manufacture and assembly
of the globoidal cam mechanism.
Abstract: By incorporating a prey refuge, this paper proposes new discrete Leslie–Gower predator–prey systems with and without Allee effect. The existence of fixed points are established and the stability of fixed points are discussed by analyzing the modulus of characteristic roots.
Abstract: In this paper we study a food chain model with three trophic levels and Michaelis-Menten type ratio-dependent functional response. Distinctive feature of this model is the sensitive dependence of the dynamical behavior on the initial populations and parameters of the real world. The stability of the equilibrium points are also investigated.