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In the present study, we investigate the roles of fear, refuge and hunting cooperation on the dynamics of a predator–prey system, where the predator population is subject to harvesting at a nonlinear rate. We also focus on the effects of seasonal forcing by letting some of the model parameters to vary with time. We rigorously analyze the autonomous and nonautonomous models mathematically as well as numerically. Our simulation results show that the birth rate of prey and the fear of predators causing decline in it, and harvesting of predators first destabilize and then stabilize the system around the coexistence of prey and predator; if the birth rate of prey is very low, both prey and predator populations extinct from the ecosystem, and for a range of this parameter, only the prey population survive. The fear of predators responsible for increase in the intraspecific competition among the prey species and the refuge behavior of prey have tendency to stabilize the system, whereas the cooperative behavior of predators during the hunting time destroys stability in the ecosystem. Numerical investigations of the seasonally forced model showcase the appearances of periodic solution, higher periodic solutions, bursting patterns and chaotic dynamics.

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This paper proposes to study the concept of similarity and its use in the design of fuzzy system. The concept of similarity relation is effectively used in fuzzification of crisp values. Similarity index is used in measuring approximate (graded) equality of fuzzy sets over a given universe of discourse. It is proposed to use such an index in modifying a fuzzy relation. Different similarity measures in the literature are elucidated, and a comparative study between different pairs of fuzzy sets is presented. One of these similarity measures has been used successfully in rule selection and modification of a fuzzy relation. In the process, a number of modification schemes based on different logic have been extensively studied for different reasoning mechanisms based on the same data and results are tabulated. A specificity-based approach to defuzzification is also presented, which is found to be suitable for similarity-based fuzzy systems. The results are illustrated with the behaviour of a direct current (DC) shunt motor.