THE VOLTERRA INTEGRAL EQUATIONS CONSTITUT A FUNDAMENTAL ANALYTICAL TOOL IN MORDEN ECOLOGY, THERMODYNAMICS AND ECONOMICS

Classical differential models are not always adequate for addressing problems in physics, ecology, and economics. Unlike differential equations, in which the rate of change depends on the instantaneous state of the system, integral equations introduce a kernel that describes how past states influence the present. Modern science has extensively employed Volterra integral equations with distributed-effect kernels (in time and space), for which a well-developed theoretical framework exists. The form of the kernel is determined by the nature of the underlying process. The choice of core reflects the different levels of system memory: shortterm, spatial, or long-term. Integral models with distributed-effect kernels provide more realistic predictions and support the development of effective control strategies. Volterra integral equations are widely used to model systems with memory and temporal evolution. “Environmental memory” is generalized to the concept of “investment memory” in economics.