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It is showed that the solutions of zero-limit nonlinear dispersive equation expanding in limit Fourier series with threshold KG wave number exhibit unexpected features.The study is carried out in zero-limit dispersive Benjamin-Ono equation.For large KG,smooth initial wave profile develops into small-scale structures like shock or pre-shock with strong vorticity gradients which interact with fluid particle motion.Discrete initial condition can also introduce the shock structures into systems.The interaction leads to resonance of a localized short-wavelength oscillation,called tyger.Resonances of tygers,explained by wave-particle resonance,are found in simulation of zero-limit Benjamin-Ono equation,when discrete Galerkin modes are chosen.Tygers emerge at the appearance of shock or pre-shock whenever continuous or discontinuous initial wave profile is selected.After their births,tygers are growing larger with the resonance domain expanding.Oscillation of the whole domain are also explored with the gradual loss of symmetry and ended by a local chaotic behavior.Anti-tyger is also observed before the birth of a pair of tygers with specific continuous smooth initial condition.At last it is shown that dispersion will prevent tygers no matter how small it is.