We investigate the dynamical behaviour of two limit cycle oscillators that interact with each other via time delayed coupling and find that time delay can lead to amplitude death of the oscillators even if they have the same frequency. We demonstrate that this novel regime of amplitude "death" also exists for large collections of coupled identical oscillators and provide quantitative measures of this death region in the parameter space of coupling strength and time delay. Its implication for certain biological and physical applications is also pointed out.Comment: 4 aps formatted revtex pages; 3 figures; to be published in Phys. Rev. Let

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Experimental observations of time delay induced amplitude death in a pair of coupled nonlinear electronic circuits that are individually capable of exhibiting limit cycle oscillations are described. In particular, the existence of multiply connected death islands in the parameter space of the coupling strength and the time delay parameter for coupled identical oscillators is established. The existence of such regions was predicted earlier on theoretical grounds in [Phys. Rev. Lett. 80, 5109 (1998); Physica 129D, 15 (1999)]. The experiments also reveal the occurrence of multiple frequency states, frequency suppression of oscillations with increased time delay and the onset of both in-phase and anti-phase collective oscillations.PACS numbers: 05.45.Xt, 87.10.+eCoupled limit cycle oscillator models have been extensively studied in recent years because of the useful insights they provide into the collective behaviour of many physical, chemical and biological systems [1][2][3][4]. One of the simplest such models, the so-called Kuramoto model [1], which retains only the phase information of each oscillator and is valid in the limit of weak mutual couplings, displays a spontaneous transition to a synchronized collective state of a single frequency when the coupling strength exceeds a critical value. Similar collective behaviour is observed in many natural systems, such as the synchronous flashing of fireflies, the phase locking of cardiac pacemaker cells, and the collective chirping of crickets [4]. Phase locking has also been demonstrated experimentally in arrays of coupled nonlinear electronic circuits [5]. When the coupling becomes stronger, amplitude effects become important and give rise to other interesting collective states, such as that of amplitude death in which the various oscillators pull each other off their periodic states and collapse to a state of zero amplitude. The condition for such a state to occur is for the oscillators to have a broad dispersion in their natural frequencies and for the coupling strength to exceed a threshold value. Thus, as has been pointed out in a number of theoretical studies [6], a collection of identical limit cycle oscillators cannot display amplitude death. However, more recent investigations [7] indicate that the presence of finite propagation time delays in the coupling removes this restriction and predict the possibility of inducing the death state even in a system of two coupled identical limit cycle oscillators. Time delay is ubiquitous in most physical systems due to finite propagation speeds of signals, finite chemical reaction times, finite response times of synapses, etc., and its influence on the collective dynamics of coupled systems can have wide-ranging implications [8]. It is important therefore to establish the experimental feasibility of such a death phenomenon.In this Letter we present experimental observations on time delay induced death in two coupled nonlinear circuits that are individually capable of exhibiting limit cycle oscillations. A specially des...

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Field experiments were conducted during [2005][2006][2007] to test effects of nineteen treatments on turmeric rhizome yield in Alfisol at Utukur and Inceptisol at Jagtial in India. The treatments were comprised of nitrogen (N) at 0, 60, 120 and 180 kg ha −1 ; phosphorus (P) at 0, 40, 80, and 120 kg ha −1 ; and potassium (K) at 0, 50, 100, and 150 kg ha −1 . Application of 180-120-100 kg ha −1 NPK gave maximum yield of 4302 kg ha −1 in Alfisols, whereas application of 120-80-100 kg ha −1 gave 4817 kg ha −1 in Inceptisols. Regression and principal component (PC) models were calibrated through soil-plant-fertilizer variables. The regression model gave significant R 2 of 0.75 in Alfisols compared to 0.88 in Inceptisols, whereas the PC model explained variance of 66.5 percent in Alfisols and 76.3 percent in Inceptisols. Regression model through PC scores gave R 2 of 0.54 in Alfisols and 0.47 in Inceptisols. Maximum sustainability yield indexes of 58.8 and 55.5 percent by 180-120-120 kg ha −1 (Alfisol) and 67.1 and 60.6 percent Color versions of one or more of the figures in the article can be found online at www. tandfonline.com/lcss. 781 782 D. V. Ramana Reddy et al. by 120-80-100 kg ha −1 (Inceptisol) were attained based on regression and PC models respectively.