Generalized Lotka-Volterra (GLV) equations are important equations used in various areas of science to describe competitive dynamics among a population of N interacting nodes in a network topology. In this Letter, we introduce a photonic network consisting of three optoelectronically cross-coupled semiconductor lasers to realize a GLV model. In such a network, the interaction of intensity and carrier inversion rates, as well as phases of laser oscillator nodes, result in various dynamics. We

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... dy the influence of asymmetric coupling strength and frequency detuning between semiconductor lasers and show that inhibitory asymmetric coupling is required to achieve consecutive amplitude oscillations of the laser nodes. These studies were motivated primarily by the dynamical models used to model brain cognitive activities and their correspondence with dynamics obtained among coupled laser oscillators. Competition and cooperation occur in many networks/societies where constituent nodes/populations directly or indirectly interact with each other. Such phenomena have been observed in various fields such as ecology and evolution [1], dispersive environments resulting in unique spatial patterns among their populations [2], frequency-dependent cancer progression and dynamics [3, 4] , and collective oscillations in genetic networks [5] . Moreover, during the last few decades, scientists have used these dynamics to describe cognitive processes such as sequential learning and decision making in the brain [6, 7] . Such dynamics have been further incorporated in cellular neural networks [8] . To mathematically model the interactions between the populations or nodes of a dynamic network, different models and equation sets have been introduced. One important set of such equations used to express and predict the fate of an ongoing competition in a population of N interacting nodes within a network topology is the set of generalized Lotka-Volterra (GLV) equations [9] [10] [11] . This set of ordinary differential equations has several dynamical solutions corresponding to the results of nodal competitions. By changing the interaction rates between nodes, the Lotka-Volterra equations are capable of producing simple attractors, stable heteroclinic channels (SHCs), limit cycles, and even chaotic solutions. These dynamics have been suggested to model neural population dynamics, as well as single neuronal activities [12] . In the context of laser physics, they have been used to describe the interaction between modes of multimode lasers where modes are coupled to each other through cross-saturation coefficients [13] . However, in multimode lasers, these parameters are inherent to the laser structure and are fixed, preventing us from exploring and switching between different dynamics and, consequently, mapping physical problems onto the system. In this Letter, we introduce a network consisting of coupled lasers designed so that the rate equations of the semiconductor lasers resemble Lotka-Volterra equations. It should be noted that since semiconductor lasers present a carrier density-dependent refractive index, the phase and amplitude of the optical fields are coupled to each other. Thus, we propose to exploit the physics of a complex amplitude of coupled arrays of laser oscillators to formulate complex Lotka-Volterra (CLV) equations. In such a system, using optoelectronically coupled semiconductor lasers, competitive dynamics can be achieved in an optical platform. On the other hand, lasers with feedbacks are highly nonlinear systems allowing the emergence of more complex dynamical behavior. Here, we investigate different regimes of competition/cooperation among the laser output photon numbers and optical phases. Further, we study the influence of asymmetric coupling strength and frequency detuning between semiconductor lasers and demonstrate winnerless, winner-takes-all (WTA), as well as winner-shares-all (WSA) competitions. We also demonstrate partial synchronization among laser nodes and show bifurcation of heteroclinic channel all the way to a chaotic regime. The objective of our model is to realize a photonic platform that is governed by Lotka-Volterra equations. To achieve this, we propose a network of N laser nodes interacting via mutually non-symmetric inhibitory connections [see Fig. 1(a) ]. These connections are realized through optoelectronic feedback loops [14] [15] [16] [17] . We assume that the feedback delay time is negligible, 5238 Vol. 41, No. 22 / November 15 2016 / Optics Letters Letter 0146-9592/16/225238-04 Journal