Indian Institute of Technology Palakkad&nbsp;(IIT Palakkad or IIT PKD) is a public autonomous&nbsp;engineering&nbsp;and&nbsp;research&nbsp;institute located in&nbsp;Palakkad,&nbsp;Kerala. It was&nbsp;one of the five new&nbsp;IITs&nbsp;proposed in the&nbsp;2014 Union budget of India. The campus was inaugurated on 3 August 2015. The institute has 94 faculty, 978 students, and 63 non-teaching staffs.

IT Palakkad currently offers four-year Bachelor of Technology (B.Tech) and two years MS programmes in 8 different engineering disciplines including&nbsp;Computer Science, Electrical, Mechanical, Civil among others.

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IIT Palakkad

We revisit the simplest walker studied earlier by Garcia and co-workers. We extend the small-slope stability analysis to second order, substantially improving accuracy, and also provide some details left out of the earlier work. We develop an alternative (reverse) approach for the stability analysis, which involves shorter calculations: for stability analysis upto any given order, the new procedure requires calculations to one order less than the previous (forward) procedure. The stability results obtained by the two methods are, nevertheless, equivalent.

Department of Mechanical Engineering

World University root node

Nonlinear Dynamics

An alternative stability analysis technique for the simplest walker

We study small perturbations of three linear Delay Differential Equations (DDEs) close to Hopf bifurcation points. In analytical treatments of such equations, many authors recommend a center manifold reduction as a first step. We demonstrate that the method of multiple scales, on simply discarding the infinitely many exponentially decaying components of the complementary solutions obtained at each stage of the approximation, can bypass the explicit center manifold calculation. Analytical approximations obtained for the DDEs studied closely match numerical solutions.