C. G. Chakrabarti

DETERMINISTIC AND STOCHASTIC ANALYSIS OF A NONLINEAR PREY-PREDATOR SYSTEM

The paper deals first with the deterministic analysis of stability and bifurcation of a non-linear model prey-predator system and then with the critical analysis of nonequilibrium fluctuation and stability of the model system under random perturbation including the comparative study of both deterministic and stochastic criteria of stability of the system.

A nonlinear two-species oscillatory system: bifurcation and stability analysis

The present paper dealing with the nonlinear bifurcation analysis of two-species oscillatory system consists of three parts. The first part deals with Hopf-bifurcation and limit cycle analysis of the homogeneous system. The second consists of travelling wave train solution and its linear stability analysis of the system in presence of diffusion. The last deals with an oscillatory chemical system as an illustrative example.

Non-equilibrium thermodynamics of Lotka-Volterra ecosystems: Stability and evolution

A non-equilibrium thermodynamic theory of generalized Lotka-Volterra ecosystem has been presented. The main results consist of the derivation of a generalized expression of entropy-production for the evolutionary ecosystem and the study of its role in the analysis of ecological stability, succession and also in the formulation of some extremum principles characterising the evolution of the ecosystem.

Boltzmann entropy: generalization and applications.

The object of the paper is to generalize Boltzmann entropy to takeaccount of the subjective nature of a system. The generalized entropyor relative entropy so obtained has been applied to an ecologicalsystem leading to some interesting new results in violation ofexisting physical laws. The entropy was further developed to derive ageneralized macroscopic measure of relative entropy which plays asignificant role in the study of stability and evolution ofecological and chemical reaction systems.

Maximum-entropy principle: ecological organization and evolution

In the present paper, we have first studied the role of the maximum-entropy principle to explain the concept of organization of a physical system in the decreasing law of entropy with the increase of external constraints imposed on the system. We have then considered an open ecosystem (living) and determined a quantitative measure of ecological organization from the consideration of the thermodynamics of irreversible processes. Finally, we have tried to explain the evolution of the ecosystem in the light of Prigogine’s principle of “order through fluctuation.”

SHIFT OF BIFURCATION POINT DUE TO NOISE INDUCED PARAMETER

The object of the paper is to see the effect of small stochastic parametric per- turbation on a nonlinear interacting system exhibiting Hopf bifurcation. The method is based on the technique of Markov diffusion approximation.

Non-linear bifurcation analysis of reaction-diffusion activator-inhibator system.

The paper first deals with the linear stability analysis of an activator-inhibitor reaction diffusion system to determine the nature of the bifurcation point of the system. The non-linear bifurcation analysis determining the steady state solution beyond the critical point enables us to determine characteristic features of the spatial inhomogeneous pattern formation arising out of the bifurcation of the state of the system.

NON-EQUILIBRIUM THERMODYNAMICS AND STOCHASTICS OF GOMPERTZIAN GROWTH

The paper deals with the non-equilibrium thermodynamic modelling of Gompertzian growth of a population substantiated by a stochastic model of the system under random disturbance of the environment.

Dynamical entropy via entropy of non-random matrices: Application to stability and complexity in modelling ecosystems

In the present paper we have first introduced a measure of dynamical entropy of an ecosystem on the basis of the dynamical model of the system. The dynamical entropy which depends on the eigenvalues of the community matrix of the system leads to a consistent measure of complexity of the ecosystem to characterize the dynamical behaviours such as the stability, instability and periodicity around the stationary states of the system. We have illustrated the theory with some model ecosystems.