scholarly journals A mathematical model of the defence mechanism of a bombardier beetle

2013 ◽  
Vol 10 (79) ◽  
pp. 20120801 ◽  
Author(s):  
Alex James ◽  
Ken Morison ◽  
Simon Todd
Keyword(s):  
Mathematical Model ◽  
Pulsed Discharge ◽  
Defence Mechanism ◽  
Cyclic Behaviour ◽  
Realistic Parameter ◽  
Almost All ◽  
Parameter Values ◽  
Continuous Discharge

Previous studies of bombardier beetles have shown that some species have a continuous discharge while others exhibit a pulsed discharge. Here, a mathematical model of the defence mechanism of the bombardier beetle is developed and the hypothesis that almost all bombardiers' defences have some sort of cyclic behaviour at frequencies much higher than previously thought is put forward. The observation of pulses arises from secondary lower frequency cycles that appear for some parameter values. For realistic parameter values, the model can exhibit all the characteristics seen in the various species of bombardier. The possibility that all bombardiers have the same underlying defence mechanism gives weight to the theory that all bombardiers' explosive secretory mechanisms have diversified from a common ancestral mechanism.

scholarly journals MATHEMATICAL MODEL OF THREE SPECIES FOOD CHAIN INTERACTION WITH MIXED FUNCTIONAL RESPONSE

2012 ◽  
Vol 09 ◽  
pp. 334-340 ◽  
Author(s):  
MADA SANJAYA WS ◽  
ISMAIL BIN MOHD ◽  
MUSTAFA MAMAT ◽  
ZABIDIN SALLEH
Keyword(s):  
Mathematical Model ◽  
Functional Response ◽  
Food Chain ◽  
Equilibrium Points ◽  
Dynamical Behavior ◽  
Bifurcation Points ◽  
Dynamical Behaviors ◽  
Practical Life ◽  
Parameter Values ◽  
Chain Interaction

In this paper, we study mathematical model of ecology with a tritrophic food chain composed of a classical Lotka-Volterra functional response for prey and predator, and a Holling type-III functional response for predator and super predator. There are two equilibrium points of the system. In the parameter space, there are passages from instability to stability, which are called Hopf bifurcation points. For the first equilibrium point, it is possible to find bifurcation points analytically and to prove that the system has periodic solutions around these points. Furthermore the dynamical behaviors of this model are investigated. Models for biologically reasonable parameter values, exhibits stable, unstable periodic and limit cycles. The dynamical behavior is found to be very sensitive to parameter values as well as the parameters of the practical life. Computer simulations are carried out to explain the analytical findings.

scholarly journals Population Behavior in the Mathematical Model of the Spread of COVID19 Type SEIRS

2021 ◽  
Vol 6 (2) ◽  
pp. 83-88
Author(s):  
Asmaidi As Med ◽  
Resky Rusnanda
Keyword(s):  
Mathematical Modeling ◽  
Numerical Simulation ◽  
Mathematical Model ◽  
Everyday Life ◽  
Applied Mathematics ◽  
Living Things ◽  
Simulation Results ◽  
Parameter Values ◽  
The Mathematical Model ◽  
Disease Free

Mathematical modeling utilized to simplify real phenomena that occur in everyday life. Mathematical modeling is popular to modeling the case of the spread of disease in an area, the growth of living things, and social behavior in everyday life and so on. This type of research is included in the study of theoretical and applied mathematics. The research steps carried out include 1) constructing a mathematical model type SEIRS, 2) analysis on the SEIRS type mathematical model by using parameter values for conditions 1and , 3) Numerical simulation to see the behavior of the population in the model, and 4) to conclude the results of the numerical simulation of the SEIRS type mathematical model. The simulation results show that the model stabilized in disease free quilibrium for the condition  and stabilized in endemic equilibrium for the condition .

Condition Monitoring Technology for Connecting Part and Sliding Part of Reciprocating Compressor

2017 ◽  
Author(s):  
Yoshifumi Mori ◽  
Takashi Saito ◽  
Yu Mizobe
Keyword(s):  
Mathematical Model ◽  
Natural Frequencies ◽  
Error Function ◽  
Connecting Rod ◽  
Value Analysis ◽  
Before And After ◽  
The Difference ◽  
Bending Modes ◽  
Parameter Values ◽  
The Mathematical Model

We focused on vibration characteristics of reciprocating compressors and constructed the mathematical model to calculate the natural frequencies and modes for crank angles and proposed a method to estimate the degree and the suspicious portion of failure by difference of temporal parameter values obtained using measuring data in operation and the mathematical model. In this paper, according to the proposed method, a case study is carried out using the field data, where the data were acquired before and after the failures occurred in the connecting parts of connecting rod, to prospect the difference between each parameter value for two operating states. Inspecting resonant characteristics each in the frequency response data relating to the natural frequencies for bending modes of the piston rod, we determined two resonant frequencies, which could correspond to the 1st and 2nd mode about bending of the piston rod. To equate the calculated each natural frequency from eigen value analysis based on the proposed model with each resonant frequency, we define the error function for the identified problem, namely optimum problem. In the identified results, it is found that some parameter values have much difference and the corresponding failure could occur around the connecting rod. We could show the possibility to detect both the change of the parameter values and the deterioration parts for two different kinds of the operating states by our proposed method.

scholarly journals Parameter sensitivity analysis on a mathematical model of reepithelialization

2019 ◽  
Vol 5 (1) ◽  
pp. 81-84
Author(s):  
Jacquelyn Dawn Parente ◽  
Knut Möller ◽  
Bala Amala Kannan ◽  
Sabine Hensler ◽  
Claudia Kuhlbach ◽  
...  
Keyword(s):  
Mathematical Model ◽  
Sensitivity Analysis ◽  
Wound Healing ◽  
Chronic Wounds ◽  
Parameter Sensitivity ◽  
Parameter Sensitivity Analysis ◽  
Adhesion Coefficient ◽  
Optimal Distance ◽  
Parameter Values

AbstractReepithelialization is the single requirement to define a wound as healed when the barrier function of the skin is restored. An existing reepithelialization mathematical model (RM) simulates wound healing in vitro. This work performs a parameter sensitivity analysis on an existing RM to see how robust the model is for changing wound healing rates for application to chronic wounds (inhibition) and wound healing therapies (activation). The existing RM balances the optimal distance between cells and basal membrane segments (BMs) according to the calculation of intercellular pressure and adhesion force. The RM mimics cell behavior and their interaction by passive migration, which is the displacement of cells from its initial position. First, this work reproduces the RM. The initial case recreates the interaction of a cell with its surrounding cells, while the second case recreates the interaction of the cell with its nearest BMs. These two cases were implemented in MATLAB to estimate optimal distance, intercellular pressure, an adhesive force between cells and the BMs. The analysis computes movement vectors and new positions of each cell at different time steps. Parameter sensitivity analysis was then conducted on the adhesion coefficient, where the original value in the RM was unknown. The results obtained at the assumed original parameter values are similar to the existing RM. As a result of the parameter sensitivity analysis, increasing the adhesion coefficient increases cell movement. High basal adhesion causes passive movement of cells, which in the simulation results is seen as a cellular movement towards wound closure. The existing RM is robust to changing adhesion coefficient values which change the rate of the advancing reepithelialization front. Future work includes fitting adhesion coefficient parameter values to an in vitro wounded tissue visualized by live dyes in treatment therapy experiments.

Aromatic hydrocarbons from the Middle Jurassic fossil wood of the Polish Jura

2013 ◽  
Vol 2 (1) ◽  
pp. 82-90
Author(s):  
Justyna Smolarek ◽  
Leszek Marynowski
Keyword(s):  
Organic Matter ◽  
Aromatic Hydrocarbons ◽  
Middle Jurassic ◽  
Vitrinite Reflectance ◽  
Fossil Wood ◽  
Terrestrial Organic Matter ◽  
Weathering Processes ◽  
Diagenetic Processes ◽  
Almost All ◽  
Parameter Values

ABSTRACT Aromatic hydrocarbons are present in the fossil wood samples in relatively small amounts. In almost all of the tested samples the dominating aromatic hydrocarbon is perylene and its methyl and dimethyl derivatives. The most important biomarkers present in the aromatic fraction are dehydroabietane, siomonellite and retene, compounds characteristic for conifers. The distribution of discussed compounds is highly variable due to such early diagenetic processes affecting the wood as oxidation and the activity of microorganisms. MPI1 parameter values (methylphenanthrene index) for the majority of the samples are in the range of 0.1 to 0.5, which results in the highly variable values of Rc (converted value of vitrinite reflectance) ranging from 0.45 to 0.70%. Such values suggest that MPI1 parameter is not useful as maturity parameter in case of Middle Jurassic ore-bearing clays, even if measured strictly on terrestrial organic matter (OM). As a result of weathering processes (oxidation) the distribution of aromatic hydrocarbons changes. In the oxidized samples the amount of aromatic hydrocarbons, both polycyclic as well as aromatic biomarkers decreases.

Integrable deformations, bi-Hamiltonian structures and nonintegrability of a generalized Rikitake system

2019 ◽  
Vol 16 (04) ◽  
pp. 1950059 ◽  
Author(s):  
Kaiyin Huang ◽  
Shaoyun Shi ◽  
Zhiguo Xu
Keyword(s):  
Galois Groups ◽  
Point Of View ◽  
Integrable Case ◽  
Analytic First Integrals ◽  
Rikitake System ◽  
Constants Of Motion ◽  
Integrable Deformations ◽  
Particular Solution ◽  
Almost All ◽  
Parameter Values

The aim of this paper is to investigate a generalized Rikitake system from the integrability point of view. For the integrable case, we derive a family of integrable deformations of the generalized Rikitake system by altering its constants of motion, and give two classes of Hamilton–Poisson structures which implies these integrable deformations, including the generalized Rikitake system, are bi-Hamiltonian and have infinitely many Hamilton–Poisson realizations. By analyzing properties of the differential Galois groups of normal variational equations (NVEs) along certain particular solution, we show that the generalized Rikitake system is not rationally integrable in an extended Liouville sense for almost all parameter values, which is in accord with the fact that this system admits chaotic behaviors for a large range of its parameters. The non-existence of analytic first integrals are also discussed.

The Evaluation of Agreement Between Dynamics of Electric Wheelchair and Human Behavior

2004 ◽  
Vol 16 (4) ◽  
pp. 434-442 ◽  
Author(s):  
Shigenobu Shimada ◽  
◽  
Kosei Ishimura ◽  
Mitsuo Wada ◽  
Keyword(s):  
Mathematical Model ◽  
Computer Simulation ◽  
Stability Analysis ◽  
Human Behavior ◽  
User Behavior ◽  
Electric Wheelchair ◽  
Straight Line ◽  
Almost All

We studied the problem of interaction of movement between the electric wheelchair and the user. Almost all current products have indexes such as roll stability and operability, but such indexes do not always agree with user behavior because such indexes are static. Another problem arises from the fact that the disagreement of movement causes uncontrollable situations and turnover of the wheelchairs. We evaluated wheelchairs that consider user behavior, first in an experiment to understand the cause of disagreement among users during movement by measuring straight line ands turning, then, based on this result, derived a mathematical model for disagreement in wheelchair motion. Computer simulation, showed that vibration occurred within certain parameters. We present simple roll stability analysis of wheelchairs turning. Simulation confirmed the viability of our proposals.

A toy cosmological model with dynamical backreaction

2015 ◽  
Vol 24 (05) ◽  
pp. 1550035
Author(s):  
Ivan V. Drobov ◽  
Nikolai N. Paklin ◽  
Sergey Ph. Tegai
Keyword(s):  
Cosmological Model ◽  
Speed Of Light ◽  
Dust Shell ◽  
Peculiar Velocities ◽  
Realistic Parameter ◽  
Parameter Values ◽  
Averaged Model

In this paper, the Buchert averaging of the Dust Shell Universe is explicitly carried out. The dynamical backreaction does not vanish in such a model. Instead, it acts as the possible source of the negative deceleration. However, the parameters of the model allowing negative deceleration lead to mean overdensities with r200 > 10 h -1 Mpc and peculiar velocities as high as the fifth part of the speed of light. With more realistic parameter values the averaged model behavior is close to Friedmannian.

scholarly journals Accumulation of P elements in minority inversions in natural populations of Drosophila melanogaster

1992 ◽  
Vol 59 (1) ◽  
pp. 1-9 ◽  
Author(s):  
Walter F. Eanes ◽  
Cedric Wesley ◽  
Brian Charlesworth
Keyword(s):  
Mathematical Model ◽  
Drosophila Melanogaster ◽  
Copy Number ◽  
Natural Populations ◽  
P Element ◽  
P Elements ◽  
Chromosomal Inversions ◽  
Associated Production ◽  
African Populations ◽  
Parameter Values

SummaryThe accumulation of a transposable element inside chromosomal inversions is examined theoretically by a mathematical model, and empirically by counts of P elements associated with inversion polymorphisms in natural populations of Drosophila melanogaster. The model demonstrates that, if heterozygosity for an inversion effectively reduces element associated production of detrimental chromosome rearrangements, a differential accumulation of elements is expected, with increased copy number inside the minority inversion. Several-fold differential accumulations are possible with certain parameter values. We present data on P element counts for inversion polymorphisms on all five chromosome arms of 157 haploid genomes from two African populations. Our observations show significantly increased numbers of elements within the regions associated with the least common, or minority arrangements, in natural inversion polymorphisms.

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