Deterministic, stochastic and thermodynamic modelling of some interacting species / / Guruprasad Samanta

• Record Nr.: UNINA9910510551103321
• Autore: Samanta Guruprasad
• Pubbl/distr/stampa: Gateway East, Singapore : , : Springer, , [2021]; ©2021
• ISBN: 9789811663123; 9789811663116
• Descrizione fisica: 1 online resource (188 pages)
• Collana: Forum for interdisciplinary mathematics
• Disciplina: 570.151
• Soggetti: Biomatemàtica; Ecologia; Models matemàtics; Biomathematics; Ecology - Mathematical models; Population genetics; Llibres electrònics
• Lingua di pubblicazione: Inglese
• Formato: Materiale a stampa
• Livello bibliografico: Monografia
• Nota di bibliografia: Includes bibliographical references.
• Nota di contenuto: Intro -- Preface -- Contents -- About the Author -- 1 Dynamical Models of Single and Predator-Prey Species -- 1.1 Introduction -- 1.2 Malthus Population Growth Model -- 1.3 Logistic Population Growth Model -- 1.4 Lotka-Volterra Model of Predator-Prey System -- 1.4.1 Trajectories -- 1.4.2 Secular (or Characteristic) Equation for Determining Local Stability -- 1.4.3 Linear (or Local) Stability of the Lotka-Volterra Model -- 1.5 Stabilization of Predator-Prey System by Introduction of Intraspecific … -- 1.5.1 Linear Stability Analysis of Logistic Lotka-Volterra Predator-Prey Model -- 1.5.2 Global Stability -- 1.6 Predator Functional Response on Prey Population -- 1.7 Limit Cycles and Hopf Bifurcation -- 1.8 Jacobian Matrix or Variational Matrix -- 1.9 Hopf Bifurcation in the Prey-Dependent Predator-Prey System -- 1.9.1 Boundedness of the System -- 1.9.2 Equilibria -- 1.9.3 Stability and Bifurcation Analysis -- 1.9.4 Numerical Simulation -- 1.10 Hopf Bifurcation in the Ratio-Dependent Predator-Prey System -- 1.10.1 ; Boundedness and Permanent of the System -- 1.10.2 Equilibria -- 1.10.3 Numerical Simulation -- 1.11 Leslie-Gower Predator-Prey Model -- 1.11.1 Boundedness of the System -- 1.11.2 Stability Property of Interior Equilibrium -- 1.12 Other Modifications -- 1.12.1 Time-Delay Effects -- 1.12.2 Noise -- 1.13 Kinetics of Growth and Ageing -- 1.13.1 Dissipative Function: Basic Kinetic Equation -- 1.13.2 Kinetic of Biological Growth -- References -- 2 Dynamical Models of Single-Species System in a Polluted Environment -- 2.1 Introduction -- 2.2 Dynamical Model I of a Single-Species System in a Polluted Environment -- 2.2.1 The Basic Mathematical Model -- 2.2.2 Dynamical Behaviour -- 2.3 Dynamical Model II of a Single-Species System in a Polluted Environment -- 2.3.1 Model Construction -- 2.3.2 Routh-Hurwitz Criterion for Local Stability.; 2.3.3 Hopf Bifurcation Theorem -- 2.3.4 Stability Behaviour of the Model -- 2.3.5 Model with Double Delays -- 2.3.6 Analysis of Existence of Hopf Bifurcation -- 2.3.7 Numerical Simulations -- 2.3.8 Discussion -- References -- 3 Analysis of Nonautonomous Two Species Systems in a Polluted Environment -- 3.1 Introduction -- 3.2 Two Species Systems in a Polluted Environment -- 3.2.1 The Basic Mathematical Model -- 3.2.2 Global Stability of System (3.2.3) -- 3.2.3 Competition System -- 3.2.4 Prey-Predator System -- 3.2.5 Cooperation System -- 3.2.6 Discussion -- 3.3 Analysis of a Nonautonomous Delayed Prey-Predator … -- 3.3.1 The Basic Mathematical Model -- 3.3.2 Uniformly Persistent of System (3.3.4) -- 3.3.3 Global Asymptotic Stability of Periodic Solution -- 3.3.4 Discussion -- References -- 4 Dynamical Models of Single-Species System Under the Influence of Environmental Noise -- 4.1 Introduction -- 4.2 Influence of Environmental Noise in Gompertzian Growth Model -- 4.2.1 Gompertzian Growth with Random Birth Rate -- 4.2.2 Stationary Probability Density -- 4.2.3 Gompertzian Growth with Random Birth Rate and Crowding Coefficient -- 4.3 On Stability and Fluctuation in Logistic Growth Model in a Random Environment -- 4.3.1 Logistic Growth: Stochastic Differential Equation -- 4.3.2 Complex Stochastic Averaging -- 4.3.3 Change in Net Growth Rate -- References -- 5 Stability Behaviour in Randomly Fluctuating Versus Deterministic Environments of Two Interacting Species -- 5.1 Introduction -- 5.2 Stability Behaviour in Randomly Fluctuating Versus Deterministic Environments of the Gomatam Model of Interacting Species -- 5.2.1 Gomatam Model: Basic Stochastic Differential Equations -- 5.2.2 Discussion -- 5.3 Stability Behaviour of the Gomatam Model of Interacting Species in a Randomly Fluctuating Environment.; 5.3.1 Gomatam Model: Modified Stochastic Differential Equations -- 5.4 Stochastic Gomatam Model of Predator-Prey Species: Non-equilibrium Fluctuation and Stability -- 5.4.1 Modified Predator-Prey System (Gomatam Model): Basic Differential Equations -- 5.4.2 Spectral Density Functions -- 5.4.3 Non-equilibrium Fluctuation and Stability -- 5.4.4 Special Situation -- 5.5 Damped Volterra-Lotka Prey-Predator System in a Rapidly Fluctuating Random Environment -- 5.5.1 Damped Volterra-Lotka System: Basic Stochastic Differential Equations -- 5.5.2 Perturbation Approximation and Non-equilibrium Fluctuation -- 5.5.3 Special Case: Volterra-Lotka System -- References -- 6 Stochastic Analysis of a Demographic Model of Urbanization -- 6.1 Introduction -- 6.2 Modified Stochastic Demographic Model -- 6.3 Averages of the Populations -- 6.4 Discussion of the Stability of a Delta-Correlated Stochastic Process -- 6.5 Discussion -- References -- 7 Non-equilibrium Thermodynamics of Interacting Species -- 7.1 Introduction -- 7.2 Interacting Species: Thermodynamic Model and Entropy-Production -- 7.3 Measure of Organization and Criteria of Evolution -- ; References -- 8 Stability of a Social Group -- 8.1 Introduction -- 8.2 Mathematical Equations: Stability of Equilibrium State -- 8.3 Stability of Equilibrium State: Method of Loop Analysis -- 8.4 Thermodynamic Model and Stability -- 8.5 Stochastic Model and Stability -- 8.6 Discussion -- References.