Summary: Let \(E\) denote the class of all transcendental entire functions for \(f(z)=\sum^{\infty}_{n=0} a_n z^n\) for \(z \in \mathbb C\) and \(a_n \geqslant 0\) for all \(n\geqslant 0\) such that \(f(x)>0\) for \(x<0\) and the set of all (finite) singular values of \(f\) forms a bounded subset of \(\mathbb R\). For each \(f\in E\), one parameter family \(\mathcal S=\{f_{\lambda}\equiv \lambda f: \lambda > 0\}\) is considered. In this paper, we mainly study the dynamics of functions in the one parameter family \(\mathcal S\). If \(f(0)\neq 0\), we show that there exists a positive real number \(\lambda^{*}\) (depending on \(f\)) such that the bifurcation and the chaotic burst occur in the dynamics of functions in the one parameter family \(\mathcal S\) at the parameter value \(\lambda =\lambda ^{*}\). If \(f(0)=0\), it is proved that the Julia set of \(f_{\lambda}\) is equal to the complement of the basin of attraction of the super attracting fixed point 0 for all \(\lambda >0\). It is also shown that the Fatou set \(\mathcal F(f_{\lambda})\) of \(f_{\lambda}\) is connected whenever it is an attracting basin and the immediate basin contains all the finite singular values of \(f_{\lambda}\). Finally, a number of interesting examples of entire transcendental functions from the class \(E\) are discussed.