CHAOTIC COEXISTENCE IN A RESOURCE–CONSUMER MODEL

2019 ◽  
Vol 27 (02) ◽  
pp. 167-184
Author(s):  
DENIS G. LADEIRA ◽  
MARCELO M. de OLIVEIRA
Keyword(s):  
Lyapunov Exponents ◽  
Limit Cycle ◽  
Food Supply ◽  
Chaotic Behavior ◽  
Dynamical Behavior ◽  
Dynamic Variable ◽  
Interspecies Competition ◽  
Successive Period ◽  
Consumer Model ◽  
Rate Of Consumption

We study the interspecies competition in a simple resource–consumer model which includes the resource supply as a dynamic variable. In the model, an organism of each species needs to consume a certain minimum rate of resource (food) to survive; a higher rate of consumption is required for reproduction. We analyze the orbit diagrams and Lyapunov exponents in order to characterize the system dynamical behavior. We observe that under a periodic food supply, the system can exhibit coexistence in the form of limit cycle oscillations. For a certain parameter range, we observe chaotic behavior emerging from successive period doublings and quasi-periodicity.

scholarly journals Dynamics of the Modified n-Degree Lorenz System

2019 ◽  
Vol 4 (2) ◽  
pp. 315-330 ◽  
Author(s):  
Sk. Sarif Hassan ◽  
Moole Parameswar Reddy ◽  
Ranjeet Kumar Rout
Keyword(s):  
Dynamical Systems ◽  
Fixed Points ◽  
Lyapunov Exponents ◽  
Limit Cycle ◽  
Chaotic Dynamics ◽  
Lorenz System ◽  
Chaotic Behavior ◽  
Lorenz Model ◽  
Periodic Behavior ◽  
Chaotic Model

AbstractThe Lorenz model is one of the most studied dynamical systems. Chaotic dynamics of several modified models of the classical Lorenz system are studied. In this article, a new chaotic model is introduced and studied computationally. By finding the fixed points, the eigenvalues of the Jacobian, and the Lyapunov exponents. Transition from convergence behavior to the periodic behavior (limit cycle) are observed by varying the degree of the system. Also transiting from periodic behavior to the chaotic behavior are seen by changing the degree of the system.

scholarly journals A New No-Equilibrium Chaotic System and Its Topological Horseshoe Chaos

2016 ◽  
Vol 2016 ◽  
pp. 1-6
Author(s):  
Chunmei Wang ◽  
Chunhua Hu ◽  
Jingwei Han ◽  
Shijian Cang
Keyword(s):  
Numerical Simulation ◽  
Lyapunov Exponents ◽  
Chaotic System ◽  
Poincaré Map ◽  
Chaotic Behavior ◽  
Dynamical Behavior ◽  
Phase Portraits ◽  
Poincare Map ◽  
Topological Horseshoe ◽  
Simulation Techniques

A new no-equilibrium chaotic system is reported in this paper. Numerical simulation techniques, including phase portraits and Lyapunov exponents, are used to investigate its basic dynamical behavior. To confirm the chaotic behavior of this system, the existence of topological horseshoe is proven via the Poincaré map and topological horseshoe theory.

scholarly journals A computational framework for finding parameter sets associated with chaotic dynamics

2021 ◽  
pp. 1-11
Author(s):  
S. Koshy-Chenthittayil ◽  
E. Dimitrova ◽  
E.W. Jenkins ◽  
B.C. Dean
Keyword(s):  
Experimental Data ◽  
Dynamical Systems ◽  
Lyapunov Exponents ◽  
Parameter Space ◽  
Chaotic Dynamics ◽  
Chaotic Behavior ◽  
Computational Framework ◽  
Independent Variables ◽  
Systems Model ◽  
Small Support

Many biological ecosystems exhibit chaotic behavior, demonstrated either analytically using parameter choices in an associated dynamical systems model or empirically through analysis of experimental data. In this paper, we use existing software tools (COPASI, R) to explore dynamical systems and uncover regions with positive Lyapunov exponents where thus chaos exists. We evaluate the ability of the software’s optimization algorithms to find these positive values with several dynamical systems used to model biological populations. The algorithms have been able to identify parameter sets which lead to positive Lyapunov exponents, even when those exponents lie in regions with small support. For one of the examined systems, we observed that positive Lyapunov exponents were not uncovered when executing a search over the parameter space with small spacings between values of the independent variables.

scholarly journals Dynamical Behaviour in Two Prey-Predator System with Persistence

2016 ◽  
Vol 16 ◽  
pp. 20-37
Author(s):  
V. Madhusudanan ◽  
S. Vijaya
Keyword(s):  
Limit Cycle ◽  
Equilibrium Points ◽  
Dynamical Behavior ◽  
Sufficient Conditions ◽  
Dynamical Behaviour ◽  
Positive Equilibrium ◽  
Predator Population ◽  
Interior Equilibrium ◽  
Trivial Equilibrium ◽  
Necessary And Sufficient

In this work, the dynamical behavior of the system with two preys and one predator population is investigated. The predator exhibits a Holling type II response to one prey which is harvested and a Beddington-DeAngelis functional response to the other prey. The boundedness of the system is analyzed. We examine the occurrence of positive equilibrium points and stability of the system at those points. At trivial equilibrium E0and axial equilibrium (E1); the system is found to be unstable. Also we obtain the necessary and sufficient conditions for existence of interior equilibrium point (E6) and local and global stability of the system at the interior equilibrium (E6): Depending upon the existence of limit cycle, the persistence condition is established for the system. The numerical simulation infer that varying the parameters such as e and λ1it is possible to change the dynamical behavior of the system from limit cycle to stable spiral. It is also observed that the harvesting rate plays a crucial role in stabilizing the system.

Chaotic Oscillator Based on Fractional Order Memcapacitor

2019 ◽  
Vol 28 (14) ◽  
pp. 1950239 ◽  
Author(s):  
Akif Akgul
Keyword(s):  
Mathematical Model ◽  
Lyapunov Exponents ◽  
Fractional Order ◽  
Nonlinear Oscillator ◽  
Equilibrium Points ◽  
Dynamical Behavior ◽  
Chaotic Oscillator ◽  
State Equations ◽  
Chaotic Oscillators ◽  
Eigen Values

Many literatures have discussed fractional order memristor and memcapacitor-based chaotic oscillators but the entire oscillator model is considered to be of fractional order. My interest is to propose a nonlinear oscillator with considering only the memcapacitor element of fractional order. Hence, I propose a fractional order memcapacitor (FMC)-based novel chaotic oscillator. The complete mathematical model for the proposed oscillator is derived and presented in this paper. The dimensionless state equations are then analyzed by using the equilibrium points and their stability, Eigen values, Kaplan–Yorke dimensions and Lyapunov exponents. To understand the complete dynamical behavior, bifurcation graphs are obtained and presented. Finally, the proposed fractional memcapacitor oscillator is implemented by using the shelf components.

scholarly journals The comparative study of chaoticity and dynamical complexity of the low-latitude ionosphere, over Nigeria, during quiet and disturbed days

2014 ◽  
Vol 21 (1) ◽  
pp. 127-142 ◽  
Author(s):  
B. O. Ogunsua ◽  
J. A. Laoye ◽  
I. A. Fuwape ◽  
A. B. Rabiu
Keyword(s):  
Time Series ◽  
Lyapunov Exponents ◽  
Correlation Dimension ◽  
Chaotic Behavior ◽  
Surrogate Data ◽  
Tsallis Entropy ◽  
Electron Content ◽  
Total Electron ◽  
Dynamical Complexity ◽  
Definite Pattern

Abstract. The deterministic chaotic behavior and dynamical complexity of the space plasma dynamical system over Nigeria are analyzed in this study and characterized. The study was carried out using GPS (Global Positioning System) TEC (Total Electron Content) time series, measured in the year 2011 at three GPS receiver stations within Nigeria, which lies within the equatorial ionization anomaly region. The TEC time series for the five quietest and five most disturbed days of each month of the year were selected for the study. The nonlinear aspect of the TEC time series was obtained by detrending the data. The detrended TEC time series were subjected to various analyses for phase space reconstruction and to obtain the values of chaotic quantifiers like Lyapunov exponents, correlation dimension and also Tsallis entropy for the measurement of dynamical complexity. The observations made show positive Lyapunov exponents (LE) for both quiet and disturbed days, which indicates chaoticity, and for different days the chaoticity of the ionosphere exhibits no definite pattern for either quiet or disturbed days. However, values of LE were lower for the storm period compared with its nearest relative quiet periods for all the stations. The monthly averages of LE and entropy also show no definite pattern for the month of the year. The values of the correlation dimension computed range from 2.8 to 3.5, with the lowest values recorded at the storm period of October 2011. The surrogate data test shows a significance of difference greater than 2 for all the quantifiers. The entropy values remain relatively close, with slight changes in these values during storm periods. The values of Tsallis entropy show similar variation patterns to those of Lyapunov exponents, with a lot of agreement in their comparison, with all computed values of Lyapunov exponents correlating with values of Tsallis entropy within the range of 0.79 to 0.81. These results show that both quantifiers can be used together as indices in the study of the variation of the dynamical complexity of the ionosphere. The results also show a strong play between determinism and stochasticity. The behavior of the ionosphere during these storm and quiet periods for the seasons of the year are discussed based on the results obtained from the chaotic quantifiers.

QUANTUM CHAOS IN NON-SYMMETRIC POTENTIAL WELL IN A TILTED MAGNETIC FIELD

2004 ◽  
Vol 18 (17n19) ◽  
pp. 2752-2756 ◽  
Author(s):  
GUOYONG YUAN ◽  
SHIPING YANG ◽  
HONGLING FAN ◽  
HONG CHANG
Keyword(s):  
Magnetic Field ◽  
Quantum Chaos ◽  
Chaotic Behavior ◽  
Dynamical Behavior ◽  
Potential Well ◽  
Symmetric Potential ◽  
Tunnelling Effect ◽  
Non Linear ◽  
Spectral Statistics ◽  
Tilted Magnetic Field

In this paper, the dynamical behavior of a non-symmetric double potential well in a tilted magnetic field is studied. The classical Poincare section is given to exhibit the chaotic behavior of the system, and non-linear resonant lead to chaos. The paper has also given the energy spectral statistics which satisfies Brody's distribution, tunnelling effect develops quantum chaos and also holds back the development of chaos.

scholarly journals Assessment of Effects of a Delay Block and a Nonlinear Block in Systems with Chaotic Behavior Using Lyapunov Exponents

Ingeniería ◽  
2017 ◽  
Vol 22 (2) ◽  
pp. 240
Author(s):  
Pablo César Rodríguez Gómez ◽  
Maikoll Andres Rodriguez Nieto ◽  
Jose Jairo Soriano Mendez
Keyword(s):  
Nonlinear System ◽  
Linear System ◽  
Linear Systems ◽  
Lyapunov Exponents ◽  
Chaotic Behavior ◽  
Structural Characteristics ◽  
Largest Lyapunov Exponent ◽  
Nonlinear Characteristic ◽  
Feedback Systems ◽  
Contour Plots

Context: Because feedback systems are very common and widely used, studies of the structural characteristics under which chaotic behavior is generated have been developed. These can be separated into a nonlinear system and a linear system at least of the third order. Methods such as the descriptive function have been used for analysis.Method: A feedback system is proposed comprising a linear system, a nonlinear system and a delay block, in order to assess his behavior using Lyapunov exponents. It is evaluated with three different linear systems, different delay values and different values for parameters of nonlinear characteristic, aiming to reach chaotic behavior.Results: One hundred experiments were carried out for each of the three linear systems, by changing the value of some parameters, assessing their influence on the dynamics of the system. Contour plots that relate these parameters to the Largest Lyapunov exponent were obtained and analyzed.Conclusions: In spite non-linearity is a condition for the existence of chaos, this does not imply that any nonlinear characteristic generates a chaotic system, it is reflected by the contour plots showing the transitions between chaotic and no chaotic behavior of the feedback system.Language: English  

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