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CNN templates for image processing and pattern formation are derived from neural field equations, advection equations and reaction–diffusion equations by discretizing spatial integrals and derivatives. Many useful CNN templates are derived by this approach. Furthermore, self-organization is investigated from the viewpoint of divergence of vector fields.

The emergence of complexity is investigated from the viewpoint of the energy balance property and the divergence property of reaction–diffusion cellular neural networks.

This paper presents the nonlinear analysis of functionally graded curved panels under high temperature supersonic gas flows. The aerothermoelastic governing equations are determined via Hamilton's variational principle. The von Karman nonlinear strain–displacement relations are used to account for large deflections. The material properties are assumed to be temperature-dependent and varying through the thickness direction according to a power law distribution in terms of the volume fractions of the constituent components. The panel is assumed to be infinitely long and simply supported. The Galerkin method is applied to convert the partial differential governing equation into a set of ordinary differential equations and the resulting system of nonlinear equations is solved through a numerical integration scheme. The effects of volume fraction index, curved panel height-rise, and aerodynamic pressure, in conjunction with the applied thermal loading, on the dynamical behavior of the panel are investigated. Regular and chaotic motions regime are determined through bifurcation analysis using Poincaré maps of maximum panel deflection, panel time history, phase-space and frequency spectra as qualitative tools, while Lyapunov's exponents and dimension are used as quantitative tools.

In this note, we define four main categories of conservative flows: (a) those in which the dissipation is identically zero, (b) those in which the dissipation depends on the state of the system and is zero on average as a consequence of the orbits being bounded, (c) those in which the dissipation depends on the state of the system and is zero on average, but for which the orbit need not be bounded and a different proof is required, and (d) those in which the dissipation depends on the initial conditions and cannot be determined from the equations alone. We introduce a new 3D conservative jerk flow to serve as an example of the first two categories and show what might be the simplest examples for each category. Also, we categorize some of the existing known systems according to these definitions.