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Spatio-temporal pattern formation over the square and rectangular domain has received significant attention from researchers. A wide range of stationary and non-stationary patterns produced by two interacting populations is abundant in the literature. Fragmented habitats are widespread in reality due to the irregularity of the landscape. This work considers a prey-predator model capable of producing a wide range of stationary and time-varying patterns over a complex habitat. The complex habitat is assumed to have consisted of two rectangular patches connected through a corridor. Our main aim is to explain how the shape and size of the fragmented habitat regulate the spatio-temporal pattern formation at the initial time. The analytical conditions are derived to ensure the existence of a stationary pattern and illustrate the role of most unstable eigenmodes to determine the number of patches for the stationary pattern. Exhaustive numerical simulations help to explain the spatial domains size and shape on the transient patterns and the duration of transient states.
This paper proposes a novel non-oscillatory pattern (NOP) learning scheme for several oscillatory data analysis problems including signal decomposition, super-resolution, and signal sub-sampling. To the best of our knowledge, the proposed NOP is the
A new type of deterministic chaos for a system described by iterative two-dimensional maps is reported. The series being generated by the original map has an average upward trend while the first difference, which is the series of changes from one per
Iterated Function Systems (IFSs) have been at the heart of fractal geometry almost from its origin, and several generalizations for the notion of IFS have been suggested. Subdivision schemes are widely used in computer graphics and attempts have been
In this paper, we study limit behaviors of stationary measures of the Fokker-Planck equations associated with a system of ordinary differential equations perturbed by a class of multiplicative including additive white noises. As the noises are vanish
While equilibrium phase transitions are well described by a free-energy landscape, there are few tools to describe general features of their non-equilibrium counterparts. On the other hand, near-equilibrium free-energies are easily accessible but the